Easy decision to me, confirm damage, attempt repair if unable to repair keep space craft in orbit. Shuttle could at some point be repaired and safely returned to Earth. Crew is doomed, but space craft is not.
Admitting there might be a problem is the first step to finding a solution. It worked with Apollo 13, and who knows what the world's minds could have come up with in a week? Just the notoriety of 'saving the shuttle' would have had some of the best amateurs and professionals on the globe taking a crack at a solution--either to keep the astronauts alive until they could be evacuated, or to repair the shuttle.