I don't think you're wrong, but I want to mention another possibility.

It might just a CYA move on the part of an individual actor in middle management. The manager doesn't want to risk getting penalized for handing out "random perks", but also doesn't want to get in trouble for ignoring a "medically necessary" request.

Put another way: That seemingly arbitrary behavior might make more sense if you assume that it's intended to protect an individual, rather than to protect the corporation.

Why is "random perks" bad? Isn't the best interest of the company being making the employees happy so they are more productive?

The negativity around giving "random perks" makes it feel like you're running a prison, where the point is to punish people instead of a workplace.

I can totally see it from that angle. People will do what the must. Only then will they do what they can.

>I hated working in an open office and tried to leverage my post-dental-surgery fragility into a private office or the right to work from home.

Sounds like the employee in question was trying to get special accommodations they didn't really need and their employer was wise to their bullshit games. OP is the kind of person who makes these ridiculous authoritarian gatekeeper rules necessary.

which isn't a terrible strategy if you're trying to ration the benefit to the employees who want it the most

Not if you totally ignore the human aspect. We are not machines, and we do not like to follow (what to us seems like) pointless and arbitrary rules. It will just foster resentment.

Oh, believe me, I work at a "public" university, where even though I have tenure and near-total control over my time (in principle, not so in reality), and work like 60 hours a week, I still have to file a timesheet every month to record that I didn't spend any "sick leave." I know about resenting pointless rules.