There are several levels of thing going wrong here.
Firstly, as Brandin notes above, with a few odd exceptions the licence of a program does not affect the licensing status of the output; the status of the output is much more usually a function of the licence on the program's inputs.
Secondly, if this is really a GPL-licensed plugin, then even if the output were in some way a copyright derivative of the program, both versions of the GPL would require
that they be licenced under GPL (GPLv2 ss 1 and 2b, GPLv3 ss4 and 5b). The GPL, being a free licence, explicitly does not include any restrictions on usage and sharing (see freedoms zero and two). You don't say which version of the GPL it is, but GPLv3 explicitly forbids adding any such restrictions (GPLv3 s7), and GPLv2 disclaims any restrictions on usage (s0).
So I'm afraid this chap's claims don't stack up; even if his plugin does something odd like copying part of itself into the output, thus making the output a dervative of the program, his claim that the plugin is GPL-licensed rules out any non-GPL restrictions on subsequent usage, copying, and the like.
But as ever, IANAL/IANYL, so take professional legal advice before relying on this position.