I am not a lawyer. Take this as worth what you paid me for it. That said, I'll try to lay out my reasoning to allow you to reach your own conclusion as well.
TL;DR: Yes, legally it would appear to be allowed by the GPL.
The longer version:
The GNU GPL is a redistribution and source code usage license. Nothing more. Particularly, it never enters into the picture if you only use the software as an end user.
I'm going to use the GPL v2 as an example here, but the GPL v3 is not significantly different in this regard except for the exact language used.
I was dismayed to find that one contained embedded advertisements for a competing product while another installed lots of adware-like software on my computer and about 6 Firefox plugins of unknown purpose, each having nothing to do with the function of the software I intended to install.
As long as the source code for all GPL'd works is included, this is perfectly in line with the spirit of the license, which for our purposes is: giving you access to the source code, giving you the right to modify the source code, and giving you the right to redistribute the source code in original or modified form, for the works licensed under the GPL.
There's also nothing in the GPL that states that an installer can't install some GPL'd components and some proprietary components. Actually, that is quite expressly allowed by the so-called "mere aggregation" clause of section 2 (keep in mind that this was written in 1991, so while the technology has changed somewhat, the spirit of the text remains the same):
In addition, mere aggregation of another work not based on the Program
with the Program (or with a work based on the Program) on a volume of
a storage or distribution medium does not bring the other work under
the scope of this License.
What the license does state is that if you build something using GPL'd source code, under the GPL, you have to release the result under the GPL. Note that you may have received the source code under a different license, in which case the GPL never enters into consideration at all.
I thought GPL software was non-commercial, but found that this software was "bought" by a company, apparently wanting users to migrate to their paid products. Is this permitted under the GPL?
With one minor exception, the GPL says nothing about paid vs gratis.
That exception is that if you distribute GPL'd software without the source code, an offer must exist to offer a copy of the source code for a nominal fee. In the GPL v2, this is in section 3.b:
(3) You may copy and distribute the Program (or a work based on it,
under Section 2) in object code or executable form under the terms of
Sections 1 and 2 above provided that you also do one of the following:
(b) Accompany it with a written offer, valid for at least three
years, to give any third party, for a charge no more than your
cost of physically performing source distribution, a complete
machine-readable copy of the corresponding source code, to be
distributed under the terms of Sections 1 and 2 above on a medium
customarily used for software interchange; or,
(Above quote slightly reformatted to help the Markdown parser. My emphasis.)
Assuming that the copyright holder is not denying you a copy of the source code (which would be a quite different problem, because it would mean that to exercise your rights under the license they require that you comply with a license the terms of which you cannot possibly comply with in exercising your rights), you are also fully within your rights to rip out the relevant components and distribute a modified version, subject to the terms of the license.
So, yes, what you are describing is allowed by the GPL. You can certainly argue that it goes against the spirit of Free software, but there is nothing in the license that would disallow it, as long as the conditions of the license are met (in particular, full source code to GPL'd works being made available to the licensee by the distributor).
In any case, the copyright holder is not legally bound by the terms of the license. Consider that the license offers non-copyright-holders rights they otherwise would not have. The copyright holder can do anything they want, including stopping distributing the code or relicensing the work under a different license, provided in the relevant situations that all copyright holders agree to such a license change. (This is one major reason why the Free Software Foundation insists on a copyright assignment/transfer agreement for their software.) Microsoft's commercial software licenses don't spell out the right for Microsoft to distribute the software, because Microsoft already has that right irrespective of any license, because they have the copyright. The GPL is no different in that regard.