The operating system of a Chromebook has no influence whatsoever on any copyright material, since it's free and open source based.
The question you describe however has nothing to do with the operating system of the chromebook, it has to do with the Google Services Terms of Service.
Those are exactly the same throughout all operating systems they run on, whether MS-Windows, OSX, iOS or various GNU/Linux based distributions like CrOS and Android.
The benefit of running Google Services on open source or open source based operating systems (any open source GNU/Linux distro, including AOSP), is that there are no conflicting terms of service, so the legal situation of the user is pretty clear in every jurisdiction the user is situated, with the exception of the many users that illegally use Google Services (for instance in China), and the many users that use Google Services in the Continental EU, where Google is under moratorium to adapt its Terms of Service human rights violating behaviour, and the Terms of Service arguably are null and void under the laws of most Continental EU member states. Google has invested big into grabbing EU Commissioner seats to mitigate some of that pressure, but the EU Parliament is beyond control of corruption money and it's the Parliament that is constantly stepping up the actions against Google.
As to CrOS, the operating system the Chromebooks run on, that has no effect on any copyrights whatsoever. CrOS is an open source project, just like AOSP, that is delivered preinstalled in a non-OSS version on Chromebooks, because the Google Services are preinstalled, and those are not open source, BUT, Google makes sure that Chromebooks are user flashable to 100% open source software status, and that even includes the BIOS of those machines. The hardware specific code needed to compile a custom kernel is made available by the CrOS project, and CrOS itself is based upon Gentoo Linux. Since CrOS is built upon Gentoo Linux, it inherits the GNU/GPL software licensing, which avoids any modifications done to the system by users to affect any copyright situation, or any content ownership rights to be affected by the use of the software.
So dump GApps from any GNU/Linux distro (like CrOS or AOSP), and any possible copyright-related problems instantly go away.