This isn't the case. See the HP and MPEG-LA testimony before the FTC.
The pool agreement isn't exclusive. The members are free to license their patents through other venues, including cross licensing.
In fact, one of the points MPEG-LA made in their initial review letter with the DOJ is that he pool would not be used to force anyone to pay for a license to a patent which they were already licensed for some other means.
So a pool member only has to pay royalties iff they've been unable to achieve complete cross-licensing with the other pool members.
Is that true? I though members had to pay royalties even if they had a patent in the pool.