TL;DR: An Xbox developer confirmed this issue, so it’s probably safe to stop debating whether it’s possible or not. Blizzard staff also discussed it in another thread.
This is not accurate because your IP is not encrypted in all areas of their platform. An Xbox developer confirmed it is a known P2P issue on this Reddit post:
Hey all, we know this is a problem - we are actually phasing out P2P voice connections for party chat completely which we’ve been working on quite a bit in the background to stop this very problem - Source
Microsoft also has an FAQ related to this issue to cover the responsibility to their users. From their site:
If you play games on Xbox Live, you could experience a denial of service (DoS) or distributed denial of service (DDoS) attack. Such attacks may render your device (your Xbox console or your computer) temporarily unable to connect to the Internet or to Xbox Live. - Source
Taking a modem offline overnight (router shouldn’t matter unless it’s a combo unit) usually assigns a new IP, but that may not hold true for all ISPs or instances where static IPs are being assigned. In those cases, you’d have to contact the ISP and if they can’t help then you’d want to use a VPN to hide your real IP.
I mentioned this here and in the other thread, but for anyone skimming through: the router has to support a VPN setup, or you need to tunnel your connection through a computer, to be able to use a VPN on the Xbox.