No they don't. They may in theory on paper, but somehow in practice you don't see too many US pilots getting hired over there. I'm not going to count marriages of convenience, that's illegal and not practical for most of us.

This is actually like discussing jumpseats...you guys are saying "let me ride your jumpseat. My airline will not reciprocate but that's no reason to deny me since plenty of other airlines will let you onboard". Or maybe your airline does have a recip agreement, but all the captains will deny me anyway....hmm, that sounds like gojet.