Yes, this is true. I've wondered for years - for example - why PFA don't apply for approval to handle mods to CofA light aircraft, they've got the competence, and could provide a superb service to it's members (i.e. the GA community in general) as well as making some revenue for the association.
BGA has an M3 (or is it JAR-145?, I'm out of touch) approval to handle maintenance of CofA SLMG, so there's a clear precedent there.
The one thing we should all be afraid off is a turf war between the various association - which would probably do nobody any good (although the odd skirmish probably sharpens them all up). It should be a given that the associations should be taking tasks from CAA, not each other.
G