What does a 5.5 VDC rating on a super capacitor imply?
It's with respect to the capacitor failing, possibly in a dramatic and smoky manner.

Basically, a supercap, like a normal capacitor, will fail in some manner when you try to store too much energy in it (by trying to put too high a voltage on it).  Exactly how depends on the construction.

Check the Wikipedia article on supercaps for details on the failure mechanism, or go web-searching.