First of all, Scout units SHOULD backpack! Many do not. So kudos to you and your troop for hitting the trail.
Backpacking with a Scouting unit and backpacking solo or with some friends are very different beasts because their aims and methods are different. Scouting aims for character development, good citizenship, and physical fitness via outdoor activities as a patrol. The patrol is key; it is the fundamental unit of scouting. If you are not working as part of a patrol then you are not scouting.
Buy the Backpacking Merit Badge pamphlet, or get one from your troop's library, or borrow one from a MB counselor, and read it. It is all about being part of what the pamphlet calls a "trek crew." Some of the requirements are:
– define limits on the number of backpackers appropriate for a trek crew
– describe how a trek crew should be organized
– show how to pack your personal gear and your share of the crew's gear and food
– conduct a pre-hike inspection of the patrol and its equipment
Crew gear and techniques are somewhat different than individual.
So, yes, it is unscoutlike to not be part of the troop or patrol for the simple reason that scouting happens in patrols. Solo backpacking is a wonderful thing. You should do it. Crew backpacking is a wonderful thing too.
Also, a scoutmaster forcing one scout to carry another scout's gear because the second scout packed poorly is total crap.

