As I read 310.15(B)(6), it is for services or feeders that supply the main power to a residence. Using 310.15(B)(6) for any other feeder is not correct, and table 310.16 needs to be used. The only other way to use 310.15(B)(6) is for _any_ feeder in a residence is that no feeder is required to be larger than the service or feeder conductors.
So a feeder to a subpanel in a garage needs to be sized with 310.16, since a garage is not a residence, even if the garage is part of a residence. If you have a 100A service with conductors sized using 310.15(B)(6), and a 100A feeder to a garage, then the 100A feeder would be the same size as the 100A service. It isn't clear from your posts if this feeder supplies the bulk of a residence.
Congrats on getting the inspectors to see the light on the larger breaker downstream!
-Jon
