At the end of the day, if even ONE person demonstrates scientific or engineering knowledge that shows a serious safety concern, then why would you actively choose to ignore it. Period.
NASA management - whether it be by organisational process and or personally identifiable decision making - failed in their responsibilities in spectacular fashion!
I do not believe that if someone knew with 100% certainty that Challenger would blow up that it would ever have launched. The trouble came in in the judgment of that risk. In this case, from what I've read, they got it wrong - very wrong.
You can argue about how certain they have to be, or how negligent people were to ignore estimated failure probabilities of whatever magnitude. But it's not like someone says, "this will blow up 85% of the time, period. Make a call." It's more subtle, complex, and less concrete than that.
1. Note that this is not equavlent to "if it blew up, they got it wrong.". Sometimes the small, properly calculated risk blows up on you just because you're unlucky - which is different from a miscalculated risk blowing up on you.
O-rings are supposed to seal on compression, not expansion.
As it is now, the O-rings are getting blown out of their tracks but still managing to seal the whole assembly quickly enough.
The above unplanned behavior, which is the only thing preventing a hull loss (and a crew loss since there's no provision for escape) is sufficiently iffy that sooner or later we're likely to run out of luck.
(I'd also add about the Columbia loss that NASA had a "can't do" attitude towards the problem they observed of the foam hitting the wing. Hardly a "crew first" attitude.)