Absolutely true, hence the assumptions. It also assumes the OP's prior pay wasn't atypically high e.g. to fill a very specific need such as self driving computer vision refinement.
I wouldn't consider a 10-15% dip a "minor" one, though. That's consistently tens of thousands of dollars in the top ten US metro markets for these roles.
Hiring manager here. Assuming you successfully demonstrated these skills during the interview process, the pay cut probably shouldn't have happened.