Just too add: Water need not literally overtop the visible structure. The top few feet of the dam are not totally waterproof. Water pressure will get through material which is pourous enough to deal with rainwater and such. Rather than waves overtop, failure will star with small flows bleeding through near the top. These may run down inside the dam a little, only appearing on the surface a ways down the far side.

Here's a small-scale, but somewhat-satisfying view of what happens when an embankment dam is compromised.

Where?

Must be very small-scale, less than 1 pixel.

Here's one video showing the danger.

https://youtu.be/tkOBmiyTfEQ?t=8m20s

Basically, when the dam over-tops the water will cut a channel into which a little more water will flow and cut a little deeper into which more flows...and on and on.

It's a run away failure and cannot be stopped.

Here's a quicker example of how just a tiny breach at the top will drain the entire dam:

https://www.youtube.com/watch?v=hmKLxoAPU1c

Note in the first video it's the over-topping that causes the initial erosion/breach rather then the artificial one in the second video, but the mechanism of further failure is essentially the same.

I'm not sure the exact construction of the Oroville dam but it's clear the emergency spillway was concrete lined at the top likely with this sort of failure in mind.

I'd be surprised if the main bulk of the dam didn't have at least some measures to stop this kind of failure but someone with knowledge of it's construction can chime in on this point.