It would be sent to whatever process is attached to the current pseudo terminal. (When I said "remote" I was more referring to the SSH scenario, but the mechanism is the same...)

Ok, so that means the remote vs local logic doesn't apply. In fact none does. The demarcations are arbitrary. Cmd is randomly used and ctrl is randomly used. Even if there is a remote vs local rule, why not make ctrl do something for local programs? Do you use a separate keyboard for your ssh and another one for email? No. The keys switch contexts according to the active program.