O.K, does collision cover you in this scenario?

you get rear ended, and the other driver does have full coverage but comes up with a good lie and is deemed not at fault by her insurance company. At the same time, your insurance company says your not at fault. will collision cover something that is not your fault, but at the same time the other drivers insurance company says their not at fault? is this some kind of insurance gap, or conundrum that must be settled in court?