One of the reviews I read though is that the service was lacking from using the services from Amex. He did say it was not Amex's fault as they were helpful and put out the call to dispatch right away, but it took over 1.5 hours for the guy to get a truck (he assumed it was because the Amex roadside assistance network was not as large/developed as AAA's in his area).
AMEX used to -- may still, I don't know -- hire a contractor company to do the actual dispatching. They're the ones that have relationships with, and in some places contracts with, the service providers. You call amex, amex calls them, they call a towing company. If you're in an area when the firm doesn't have an established provider, either because they don't do much business there or because who they were using closed or dumped them, they can be reduced to looking at the phone book and making cold calls.
If the service provider they have or end up calling is busy, you're going to wait. That's how almost all road service providers work, whether from a CC, the car company, or an auto club.
AAA do the same thing, they're just the biggest game, and have the highest volume of calls. They don't pay their contractors well, though, so they tend to have less than the best contractors. AAA also used to insist that their calls got priority over other calls, and probably still does.