I don't see the contradiction. Stallman would agree that the GPL isn't ideal; he'd say it's a hack designed to twist our broken legal system into respecting our fundamental freedoms. The GPL is almost an anti-license, since it exists solely to do the exact opposite of what copyright laws and licenses are intended to do (restrict freedoms).
Put another way: yes, it's using the system, but any attempt to change the system from within is, by definition, 'using the system'.
If our laws deemed proprietary software licenses to be non-enforceable, I doubt anybody (Stallman included) would see the need for the GPL.