Before...about a year ago (give or take), "high floor" was mostly limited to hotels with...er...actual high floors (e.g. the HR Vancouver). I've seen it show up at the HR Orlando International a few times as well, but this was the most egregious.

FWIW as I think I mentioned I was promptly put in a 5th floor room (I would have raised polite hell with corporate if I'd been stuck on floor two with a "high floor" booking) and I made it clear to the staff that I was more standing on a bit of principle than anything else. The sad part is that if they'd just charged me the higher rate as an element of revenue management I wouldn't have blinked; it's more that they're playing games that bugs me.

With that being said, I'm actually inclined to call and grumble a bit as-is...there really needs to be at least an understanding of what counts as a high floor; ideally Hyatt would lay out a minimum (e.g. "High floor means on no less than the sixth floor unless a waiver has been granted due to unusual design elements* and also means in the upper third of floors in the hotel"). I'm waiting for some 3-4 story property to claim a "high floor" rate...

*The HR OIA comes to mind here...the building is nominally about ten stories high but the layout is complicated and I'm pretty sure there's at least one double-level hidden in there somewhere.