My understanding is that in our troop only the SM, ASMs, and the JASMs can sign off on requirements. Since the JASM hasn't gone on any of the activities (he does regularly attend the meetings) since my son has joined, he has less of a relationship with him than he does with the SM and ASMs.
With regards to only leaders signing off on requirements being indicative of a troop run by the troop method as opposed to the patrol method, I would say that our troop is a hybrid. We have strong patrol identies and use new scout patrols that stay together for the duration. On campouts, we use the