Also if I set the refresh rate to something higher than the processor can handle (simulating a crappy computer) it also starts to get backed up and eventually goes out of control.
You've made a mistake somewhere. The system which HrdNutz demonstrates is the same theory as the one you later link to on gaffer.org. The accumulator stuff really isn't hard, but I'm not sure I can explain it better than he does.
It's really just fixing the interval between updates and rendering as often as you can. If you can render ten times for every one update, you do, and if you need to update twice (or more) before rendering then you do that instead. The accumulator is only there because you can't do 2 and a bit updates, because the timestep is fixed. So you just keep the remainder in the accumulator because otherwise, it would go out of step if you threw away the left over time.