I think he is right. One of the places google servers are used is captive portal checks [1]. Here is a, albeit not very deep, thread discussing how to disable it and you can easily find reports of losing internet access on lineage if you block google addresses on your network. Otherwise a connection to google servers is made every hour or so.

I remember reading, that this is not the only place in LOS, that google servers are used, but I never looked into it.

1: https://forum.xda-developers.com/t/guide-how-to-avoid-the-ca...