According to NASA they lose tiles all the time, so far it has never caused a safety problem. Everything they knew told them that this was no different. They trusted the math they used all the time and were possibly wrong.
About an EVA, remember their calculations told them there was no safety problem, so they were probably not willing to risk the life of an astronaut just to check a few tiles.
I pray that this was just an accident, that negligence did not contribute to this disaster. NASA's only failure may have been the failure of imagination. They failed to imagine that their external fuel tank had design problems.
Keep in mind that a while a mid-launch abort was possible, they didn't know about the debris until a few days later. Try to accept the fact that even if they did find out that there was severe tile damage, the outcome of this flight would not have changed. The only thing that would change is that they would know the cause of this accident.
They have already stated that they could not change the trajectory of re-entry, because they already use the optimal trajectory to minimize stress on the shuttle.
I think you'll agree with me that if NASA actually thought that this debris posed a safety issue then they would have done everything possible to find out. Remember hindsight is always 20/20.
For their calculations. They know enough of physics to be able to calulate every little thing about the debris to make it reliable and not "guess work". The problem is that they may have trusted the calculations too much and went on the assumption of where the debris struck instead of assuming a worse-case scenario. So even though the math was correct, the starting assumption may have been bad. With a bad assumption you can quadruple check it, you'll still get the wrong answer.
On a side note, being a resident of Central Florida. Over the past few years I have taken it for granted; the ability to go outside and watched a shuttle launch, which I did for this last flight, or hearing/feeling the twin sonic booms when a shuttle returns safely. Never again.
I pray that at the end of this investigation the problem will be solved, and NASA gets back to flying. Anything less would mean these 7 brave souls died in vain. If you ever have an oppurtunity to see a future launch, take it. It is truly a spectacular sight, especially the night time launches. Television can't touch seeing it in person.