The ISS and Columbia were on different orbital inclinations relative to the Earth's equator. The ISS orbit ranges further north and south than the normal shuttle orbit. To shift Columbia's orbital inclination to match the ISS would require an enormous amount of cross-track delta-v, more than the shuttle's OMS fuel supply can support. Try as they might, they never could have matched orbit with the ISS.
Why are the oribital inclinations different? NASA made that decision when Goldin decided to bring on the Russians as ISS partners. They needed the greater inclined orbit to support launching modules/crews/supplies with Russian boosters. Not only did this change the ISS-support orbital inclination, it also reduced the available orbiter ISS mission payload since additional fuel is required to reach orbit because the inclined orbit loses some of the advantage of using the Earth's east-west rotation.
Bottom line: Columbia could not have reached the ISS.
That adds to the 'it doesn't smell right' when they kept insisting that it made no sense to look for tile damage caused at launch, because they have no capability to repair tiles in orbit...
Something tells me, that might have originally been said about Apollo 13, but when faced with the situation they figured out a way, to bring them back.