I think that is almost certainly false. Do you have a source?
According to [1], OEMs can use Android trademarks as long as they conform to the Android compatibility standard, which doesn't require a license for the Google Mobile Service (Google Play, etc) [2]. If you do want to brand it as an Android device, you largely just have to maintain compatibility with the Android ecosystem regardless of whether you distribute Google apps. If you don't want to use the Android trademark (which is independent of the source code), you don't have to do anything.