One more note for any other travellers running into this issue:
My ex-Canada Basic Economy ticket has the following endorsement line: NRF-BE/NOCHGDAFTDPT/NOASR
vs
It appears from a few searches, that carry-on restricted BE tickets have and additional endorsement (which mine does not have): NONREF/NOCHGS/NOCBBG/NOASR
Of course, given the inconsistency on the website and during the sale process, UA gate agents may be under a similar misapprehension about what is permitted. So the proof will be in the pudding on the day of travel...