I don't think that's quite right. The GPLv2 makes no mention of trademarks [0], and the GPLv3 mentions trademarks only to clarify that you may be protective of them, independent of the terms of the GPLv3.

If you license under GPL, you're still free to be protective of your trademarks.

This makes sense given that although Mozilla like to use their own licence, they've been careful over the years to either release under the GPL as well, or to use a licence of their own which has been constructed to be GPL-compatible [2]. Clearly, the GPL didn't force Mozilla to be permissive with their trademark.

[0] https://www.gnu.org/licenses/old-licenses/gpl-2.0.txt

[1] https://www.gnu.org/licenses/gpl-3.0.txt

[2] https://en.wikipedia.org/wiki/Firefox#Licensing