I don't see how you've proven the illegitimacy of my analogy.

It's really the same argument you're making. Perhaps there are Al Qaida affiliated cells that are only Al Qaida affiliated in name and ideology but do not receive funding or orders from anyone else.

In any case there are people that identify as being members of Al Qaida (Al Qaida proper or affiliated groups).

I don't see what, effectively, is the difference between a monolithic organizations and a heterogeneous group of organization that have a shared ideology.

I think this is what you're saying that Al Qaida is but I don't see how this distinction is significant for any intent or purpose.