Check this out & tell me what you think.

I think most caulking compounds would rub or peel off just as much as the Eternabond tape. I'd look instead for some other tape to bridge and protect the Eternabond edge; foil duct sealing tape (not the silver-colored fabric stuff often called duct or duck tape) might be a good option to try.

I would also look at the construction under tape. It may in fact turn out that the tech was telling the truth, and the tape not adhering well is not a serious issue. It could also be that he or she was simply avoiding unpleasant work, of course.