A pu'i claim is that at the time (PU) expressed by the rest of the tense, the potential was in a fulfilled status.
Is there any way the potential can be in a fulfilled status other than {pu ca'a}? If not (and I can't think of any) then pu'i <==> ka'e je pu ca'a (this {pu} of course is relative to whatever time is expressed by PU in the rest of the tense, so for example ba pu'i <==> ba ka'e je ba pu ca'a).