It's similar to sports team management - sure the manager is rare and more experienced, but they're not burning their mind off trying to meet irrational deadlines. The stress of management mostly comes from team issues, so I'd think paying them more would solve a lot of problems.
But it's also sort of a hierarchy thing.
To answer the question, I’ve been in this position and it can happen especially when the manager is in a less well paid city/location. Didn’t create tension but did make me realize location/market matters so much more than skillset with respect to compensation.
Let me guess, you're a programmer.
Programming actually seems to pay better in third world countries, though, as there's a shortage for specific skill sets, as opposed to developers with 20 years experience who can put together a full stack PHP site or build telco systems, but haven't done Angular.