The argument is really only with certain arts that are considered to have ineffective training methods, not with traditional martial arts per se: you won't find too many MMA people saying bad things about judo and knockdown karate, for instance, because their training methods are physically rigorous and involve a great deal of resistance from your sparring partner in a situation reasonably close to an actual confrontation.
The problem as proponents of MMA see it is not that aikido and ninjutsu are traditional arts: the problem is that they train with compliance. An aikidoka or Bujinkan ninja can get to a very high level without having his training partner *ever* make a serious attempt to resist his techniques, and this is felt to make their training ineffective.