I think the reason that they're cracking down on this is to avoid potential overtime payments

... But what on earth does that have to do with what the person NOT working does with their day? If all they care about is overtime, then the question would be "will either person switching shifts get overtime or violate labor laws like minimum shift separations due to the switch?"

The fact that they explicitly base decisions not on the shift taker - who is more likely to receive overtime pay - but the shift giver and what they are doing OUTSIDE of work says the decision has as little to do with work as whatever you'd miss a shift for.

Literally every shift place I've worked has had pretty much the same rules - if you find someone to cover without making it everyone else's problem and there's no overtime or labor violations, who gives a f***? Crazy enough, they determined that by 1. Looking at the work schedule and 2. Checking for potential overtime work, and not by asking for a copy of my non-work-related itinerary.