Coming from a 6+ year stint in a defense contracting, I can safely say that the issue with this approach happens well before the testing. The problem more often than not occurs at the requirements level.
Bingo. The government, which took the role of integrator, kept making requirements changes, right through the week before launch. They also did integration testing ... and of course ignored that that failed hard.
I can't see any way CGI Federal et. al. could have won.
If they were all that bad we'd never get anything done.
In drafting the above I removed some thoughts about CGI Federal pushing back, since that struck me as something that probably wouldn't work in this context. But I for one have pushed back on clueless customers before, saying the usual "this change will cost time, money and/or quality".
Or, heck, I'll bet CGI did some push back, but there's no reason to believe the inexperienced bureaucrats and political appointees in HHS and CMS would have listened to them. We've been reliably told they were told it was going to hell, and there's that one fed who switching in March to "I hope it won't be a Third World experience" which I take as a sign he saw trouble on the horizon.
I would argue it happens at an even higher level the 'planning' level.
One of the basic philosophical differences between the agile and waterfall approach is that agile assumes that you cannot know all the requirements at the beginning of a project. You must start building things before all the little dirty edge cases become obvious. Additionally you don't actually know if you're going in the right direction until you have something concrete to work with, even if it's mock ups or wire frames.
What I think they should of done in this case is rolled out the site in stages, probably starting with one state that had an easy backend to work with and gradually adding complexity to the site.
I can't see any way CGI Federal et. al. could have won.