I’m not sure about Utah, but here is the first page from a recent lease in California. Every single lease I’ve signed has had this provision in one form or another, and as others have stated, if they can’t get funding from the bank for a lease they will either take it back or try to sell it to you via financing; again contingent on the being able to get the financing.
Pretty sure they would just use that car as an executive demo or loaner if it has more miles than can be leased as new.
As for the registration, again in California, they have you sign a power of attorney to take care of the DMV documents for the particular vehicle; maybe she just doesn’t have the copy and doesn’t mean that she didn’t sign that for the temp plates.
Good luck, let us know how it works out.