So the fire brigade is open to interested C-permit holders now but they don't have to join. On the other hand, the 20-45 years old voters of canton Basel-Stadt are required to serve in the fire brigade or have to pay an absence fee of up to
280 Fr./year.
I fail to see any disadvantage for C-permit holders.
Also I know that you haven't meant the burning alive thing literally, but I'd still like to add that any C-permit holder who's curious enough to join the fire brigade will stay in the auxiliary firefighting force (Bezirksfeuerwehr in canton BS) where fatalities are some orders of magnitude less likely. Once somebody decides to make firefighting his full time job, the professional education he gets is of course adjusted to the new situation.
The auxiliary fire brigade is a good choice for a hobby and I've met some interesting people and good friends there. Sure, you won't be first to fight the flames, the purpose of the auxiliary fire brigade is different: To handle big events (like floods), to relieve the professional first responders in long operations (fire source control), and depending on the proximity of the nearest professionals and your rank, the litteral cat in a tree, too. You also get paid a small compensation. Many auxiliary fire brigades are searching for volunteers, the formations in canton BS do, too... I'd like to recommend firefighting to all interested foreigners with good oral fluency in the local language.