No need to doubt his story. Very likely he took a boat, like many touring cyclist doing the Pan-American route do. It is a relatively established route.

If you really want to be self-reliant, the amazing Iohan Gueorguiev bike-raft it, but that's quite on the extreme side.

Most likely took a boat past that area.

Alaska–Ushuaia cyclists commonly take a boat around the gap. It is a bit more expensive than flying, but it allows one to claim that one did the journey entirely overland. (Recently a few cyclists have bought packrafts and paddled along the coast themselves instead of paying for someone else’s boat.) You shouldn’t think the story was “problematic”, the cyclist was validly describing the journey as typically done.

That said, there are multiple recent accounts of cyclists crossing the gap. Indeed, it is a tiresome hike-a-bike because you can’t actually cycle much, but from the account by a German cyclist I read a few months ago, I don’t recall any climbing. It’s worth mentioning that even a traversal of the gap will involve leaving land and going over water along the rivers at some points.