I really believe this was the cause, but once lift-off occurs they can't turn back, and they continued the mission, and completed it with the knowledge that there may be a problem on re-entry.
Foam insulation from the large fuel tank hit the LEFT wing during takeoff. So far, everything points to the LEFT wing having problems during the break-up.
True, they may have been in an impossible situation when they took off. On the other hand, I find myself wondering what would have happened if they'd been aware of it and had crews in space and on the ground working heroically to formulate a solution. After all, the Apollo 13 astronauts were doomed and yet which a suitable combination of luck, teamwork, and miracles they all survived.
Yeah, they probably knew. Those aboard who figured it out, perhaps days before re-entry, wouldn't talk about it. Nothing can be done about it, so just do your job.
There's plenty of people, especially Americans, who would have flown the mission against the odds anyway.