Well of course it did, and the idea is popular with those who reject SCAF but want at the same time to deny the Muslim Brotherhood - or Morsi - legitimacy. What follows is a mere suggestion why this might not be the case - to be amplified later if good evidence for the suggestion emerges.
The two most substantial accusations against the Brotherhood are (a) that it was undemocratic, because it trampled on minority rights, and (b) that it essentially deserved what it got, because it was in cahoots with the military.
The accusation that the Muslim Brotherhood did not respect minority rights has been addressed, in part, in another post. It is just false that the Brotherhood's failure to include minority parties or the 'liberal opposition' in government was undemocratic. Most governments considered fully democratic would fail this bizarre test. In the first place, majorities are no doubt unjustified in failing to honour minority rights, but this doesn't make them the tiniest bit less democratic. In the second place, supposing the opposition has rights to be included in a government simply confuses the rights of minorities with the rights of minority parties to some piece of the pie. That's important, because the former rights exist, and the latter don't. The Muslim Brotherhood certainly didn't go nearly far enough to honour the rights of minorities such as Christians and - well, not really a minority - women. That was unjustified, but it was also the will of their constituency and doesn't deprive the Morsi régime of democratic legitimacy. If you don't like that, you need to take a stand against democracy, not just the Brotherhood.
What then of the claim that Morsi or the Brotherhood were 'in bed' with the military, or 'cozied up' to them? Once we get away from metaphors, the substance of this accusation gets very thin.
Probably the reproach begins with bitterness about the Brotherhood's very late arrival in demonstrations against the régime. Since the demonstrations themselves took on the aspect of an army-people love-in, this really has nothing to do with the 'cozying up' accusation, but it's also not very telling. Unlike almost all the other demonstrators, the Brotherhood had spent decades paying with their freedom and their lives for opposing the régime, and that with almost no support from liberals or secularists. Indeed the opposition contained a significant number of Nasserists who could well be understood to have supported Nasser's murder and torture of Brotherhood militants. In these circumstances it's hardly surprising that the Brotherhood wouldn't want to stick their necks out before seeing a good chance of being on the winning side. So bitterness about Brotherhood is a bit overdone here.
It's said that the Brotherhood and the military made a 'tactical alliance', and that they 'supported' one another. Well, if they made a tactical alliance, it's only in the some very tenuous sense of the expression, because the army and the Brotherhood did NOT support one another. The Brotherhood really had no support to offer, even if they'd wanted to, and the army gave the Brotherhood no support. To suppose otherwise is to give far too much significance to words and gestures, a fatal mistake in politics.
The Brotherhood's fine phrases in praise of the military have been examined elsewhere. So have its cabinet appointments and the general claim that Morsi had real executive power that could have benefited the military. These items aside, the most important alleged example of collusion seems to be the Brotherhood's backing of the March 2011 referendum, which approved constitutional amendments sponsored by the military. In what sense was this a 'tactical alliance'?
The Brotherhood backed the referendum in part because it would help them to power: the consensus was that, the sooner real elections occurred, the greater the chances of the Brotherhood emerging victorious. But winning the election, as we've seen, didn't and, in my opinion, wasn't expected to bring the Brotherhood to power all on its own. To do that, there had to be a strong civilian state, with the military reduced to its normal role in modern democracies, a meticulously apolitical fighting force concerned only to counter external threats. Otherwise, as everyone knew (link to blog), the military would certainly rule Egypt, with no more than electoral window-dressing.
This strategy implies something many political analysts have a hard time accepting - that in revolutionary times, laws, agreements, even constitutions are mere words. I believe this was the Brotherhood's view. They were willing to concede, verbally or in writing, anything the military liked, until the time they were strong enough to unsay what had been said, until popular or democratic legitimacy enabled them to do so. For them, whatever prestige and paper reinforcement the March referendum might give the military was of little consequence. There was a choice: to accept a referendum on the military's terms or to prolong a period of instability in which the position of the military, as the guardian of order, could only strengthen. This was far more of a menace than that the opposition, which showed no sign of organizational competence, would use more time to form a serious political threat, rather than to fragment even further.
We have evidence that the army, from the very start, intended to crush the Brotherhood. SCAF was simply biding its time. To suppose that the Brotherhood wanted anything but to crush the army is to suppose them impossibly naïve. This was no Hitler-Stalin pact. The army did nothing for the Brotherhood; it stymied its attempts to govern at every turn. The Brotherhood did nothing for the army; having no power, it had nothing to offer, and had the Brotherhood rejected the referendum, the army would have been at least as strong as before. Nor did the army at any time need the Brotherhood's support. It had the gun; it had the love of the people; it had no rival that could impose order on society, let alone its will on the army. All the army wanted was some makeup, a light concealer for its dictatorial power, something to keep the Americans happy. The idea that it reached out to the Brotherhood for succor rests on the false assumption that the army was ever in trouble.
So in what sense did the Brotherhood 'cozy up' to the army? The two combatants didn't even agree on a time and place of combat - only that the time was not now. The secular opposition certainly agreed on this as well; they didn't want to confront the army at that time either. The only difference, as we've learned, is that most of the opposition didn't ever want to confront the army. So by that token, the opposition cozied up to the army too.
The 'support' the Brotherhood gave to the army is not comparable to the liberals' support. The Brotherhood gave the army nothing, not even time. The liberals actively connived to legitimize the army's rule and to de-legitimize civilian rule. The liberals actually wanted to army to overthrow the government, and said so; they went into the streets to affirm their stance. It would be absurd to place this vigorous collusion in the same category as the Brotherhood's attempts to placate the army until they could destroy it.
The Brotherhood did make a mistake. It thought it could gain broad popular legitimacy. It did not realize the depth of hatred - now all too plain - that most secularists held for Islamists: so much for the complaint that the Brotherhood did not 'reach out' enough. It did not imagine that the liberals would prefer military dictatorship to civilian Islamic rule. But to make this mistake was to try to make a genuine revolution. No one can now accuse the liberals of that.
Some of the preceding is, for now, more of a scenario than an account: it's what may have happened. But that's already enough to undermine the alleged evidence for Brotherhood-army collusion.