Okay, got it. I wouldn't call that PoS, but I see what you mean.

I think of the crux of PoS as the incentive system that keeps bad actors out -- if you act maliciously, you lose your stake.

Errr, no. That's leader election, and is not a consensus algorithm by itself. It's part of the algorithm, which is nothing like PoS at all. That's like saying UDP and TCP are the same because they send packets.

It seems disingenuous to refer to that as proof-of-stake.