I used to work places that counted all hours the same way, and figured overtime on a daily basis. It seemed pretty straightforward: here's the expected work schedule, and anything in addition is overtime.
Indeed, our Labor Dept. kept going after one employer I had, and we had to fill out extremely complicated time reports. On a typical shift, it was common for there to be four different pay rates: Base rate, shift differentials for certain hours, OT for more than 8/day, OT+ for more than 40/wk.
That seems to have gone the way of the Oldsmobile. Various Labor Department rulings, in the decades since, have resulted in most employers only counting hours actually worked towards overtime.
Paying overtime is a lot like NEC code compliance; most employers actual follow practices that are in excess of what the rules actually require.
How mean is the boss? Well, look at it this way: the USDOL isn't interested at all in upholding any agreement you might have, as long as you're getting at least the minimum wage. I've seen employers pull that one: no overtime rate at all. Complain? Amazingly enough, Immigration comes to visit.
It's real easy to believe you 'should' be paid more. In the end, you have to vote with your feet. Government isn't going to help you.
My current employer pays overtime only counting 'worked' hours. As you might guess, I wasn't too motivated to work overtime last week. A lot of what I COULD have done last week will get done this week - at time-an-a-half.
As the famous Polish Electrician Lech Walesa said: they pretend to pay us, and we pretend to work.