It's not the altitude, it's the inclination.
The inclination of a satellite is the highest latitude line the satellite passes over during its orbit. For instance, if a satellite stays over the equator, it's inclination is 0 degrees.
The ISS is about 51 degrees (if I'm not mistaken).
It takes a lot of energy to put a shuttle at 51 degrees inclination. Columbia was too heavy for a misson to the ISS. It sure wouldn't be able to reach the ISS once it was in orbit for this mission.
Now, I'm not well versed on orbital mechanics, but I don't think you can change the ISS's orbit without substancial energy either.