Although my research is just know getting to this point in history, you conclusion is essentially correct.
From what I've read so far, what happened is the Territories became States with the proviso of them becoming States is that they turn around and ceed any claims over massive amounts of land to the federal government once they became States. Several bills in the Library of Congress show the feds were selling the States the land back....piecemeal.
What better way to plump the federal coffers? As long, of course, you can ignore the fact it violated more than one provision in the Constitution and that pesky little 'under duress' thing.