Right, the fact that same interior is used is explainable, but there's really no arguing against the fact that, story-wise, Indiana Jones teaches at a separate college in Last Crusade. References to Barnett are made in the film (nonverbal or not), the name appears in the movie's various adaptations, the college is brought back in Indiana Jones in the Fate of Atlantis (which takes place shortly after Last Crusade), and the placement of college's location on the US map in that game corroborates the address seen on the package in Last Crusade (namely, that it's located in upstate New York as opposed to Connecticut for Marshall). These are not coincidences - at some point during Last Crusade's development, a decision was made to move Indy's college of employment (clearly with more attention to detail than a mere name change) for whatever reason, and it became part of canon in the time line as recognized by multiple alternate universe (but no less official) material.
The real unanswered questions are why they invented this new college in the first place (Was it just to change the pace? Did they alter this aspect of the storyline during production for logistical reasons i.e. when the real-life Marshall exterior was unavailable for filming? Was there an actual decent story-related reason for Indy switching colleges that just didn't survive beyond the script?), and why Crystal Skull chooses to confuse matters by not addressing the situation at all. The answers to these questions would satisfy my curiosity, but I've got a feeling that they wouldn't turn out to be particularly impressive.