When he talks about it being their fault, it's not that those engineers are being singled out for punishment and derision. They had to find out where the problem existed that led to the loss of Columbia, and after extremely thorough testing they believed it existed with the foam team. It's simply a matter of finding where a problem is and doing everything you can to fix it.
So it's not a personal, vindictive "your fault", its an impersonal "the problem is here, lets fix it".