Fair point, but what also matters is what is being asked by BA. I did not hear that as it happened behind closed doors.

I always travel with all my documents (with what I was told by the officers too).

BA insisted also there that the work permit is not valid for travel. Only ETA or Permanent resident card they thought was acceptable.

And no, I did never see an ETA number on that introduction letter, only had a work permit number.

Permanent residence is done now too. So no more issue.

But as a matter of fact, if these documents are fine the very next day and later that week, that is a signal that they were sufficient.