I'd go with it being your problem. The Crew leader should be decided by the crew. (Unless you are going to overrule somehow based on health and safety issues). If the crew finds they have made a mistake, the crew can either change it or live with it. The boys are allowed to make mistakes like this, and hopefully learn from them. I would expect the crew knows his level of involvement is not up to your expectations, but if you overrule their decision, then you will be making a clear statement of who is really in charge of the trek. (Depending upon the voting rules, you might ask for a vote of confidence by the entire crew since half of them voted for someone else).
I sure can't speak to the specifics of your contract, but unless removal was clearly specified I would pass on that one. In addition to the bad feelings someone, or the troop is going to be out real $ unless you have replacements lined up.
I also would not have rebuffed the older scout. This may have been a way for him to reconnect to his friends in scouting in ways that the normal troop activities do not. Even without specific conditioning training, most of the youth can handle the trek.
As an aside, while I know that many adults choose the trek for their crew, as well as too many of the other duties, many also do not.
Remember that as much as we as crew advisors would like to give the boys a perfect trek they will always remember, it isn't going to happen, and they will always remember it anyway.
Enjoy your trek.