This is more of a theory, but I think this specific Clone Cop line and one of the Bonus Maps implies that when a host body is "overwritten" with Aiden, some aspects(such as parts of their original personality or memories) of the host don't go away, even influencing how the clone acts to some regard. It would also explain the "closest descendent template" role that Clone Cop fills.
You are 100% correct. The host body consciousness is essentially overwritten. This is why we call them 'template imprints'. I believe the host of Savage 3650 has already proven to have affected his personality. Clone Cop understood how it works. The science is lost on Bad Cop, though.