Terms vary. AAA franchise auto clubs do not usually take care off off-highway, and it is up to the contracted provider whether what he'll do on your own dime. But I've always carried AAA road service since I learned in the 1960s that when the going gets tough (e.g. winter storm) AAA contractors take care of AAA calls first, before any others, whether private calls or other insurers. The AAA contract network covers a big part of the spectrum of emergency road service providers.
I also carry Good Sam ERS for my RV, for the expanded terms of service, although the network of contracted providers may be more sparse. For twelve years, I've never had to call them, so I cannot yet appraise response.
FWIW, we first carried AAA because my wife wanted the service, her family used it (and insured through the auto club). In practice, for road service, her first call was usually to me. What am I going to tell her? I'm busy, call AAA?