Of course you mean that it was too heavy to carry full-sized ISS components up to the ISS orbit. I'm pretty sure it flew above ISS altitudes on several missions.
You are correct. But don't forget the 30% penalty to reach the 51 degree orbit. Columbia's maximum payload capacity to a standard orbit is 52,500 lbs. to the best of my knowledge.
I believe, but am not sure, that that figure includes the weight of passengers, expendables, and OMS/RCS fuel as well as the junk in the trunk.