Including code from non-free libraries will make your package non-free.
Not true. The result would be illegal, not non-free. For it to be legal the whole work has to be licensed under the GNU GPL.
And what you've just said is completely untrue
,----[ The GNU General Public License - Section 2 ] | b. You must cause any work that you distribute or publish, that | in whole or in part contains or is derived from the Program | or any part thereof, to be licensed as a whole at no charge | to all third parties under the terms of this License. `----
Despite what the GPL FAQ may say,
Frankly, I trust the GPL FAQ--which is based on answers from lawyers--more then I trust what your opinion on the matter is.