A rise to 5.1 volt shouldn't cause a crash, as 5.1 Volt is a perfectly acceptable voltage for the PI to operate with. Up to 5.25 Volt is acceptable!
I do think it just means that the PI draws a less lot current than normal when that happens, and that causes less losses in cables and such.
In "operation mode" the PI itself (not counting USB devices and such) the PI draws anywhere from 400 to 700mA, depending on what its doing, with everything shut down this lowers to 100mA.
So the voltage rise is a symptom of it crashing, not a cause.
In my opinion, there could be two things happening.
1) Some code on the card causes a crash, and an immediate shutdown.
2) You have a defective PI, perhaps some solder-joint is badly soldered, and the crash happens when the PI slightly expands, due to warming up somewhat, and an electrical connection is broken.
There have been reports of the second situation, and if you have one of these (normally made in China for RS) then you should return it as defective under guarantee.