That's probably exaggeration or straight lie. There are open-source messengers who don't even require a phone number, and phone number is not legally required for registration in most countries (but, for example, in Russia you cannot signup users in a messenger without getting their phone number. So those open source messengers are technically outright illegal).

As for moderation, any post in public or private groups can be reported to moderators. As for one-to-one chats, this might not work, but you should not be chatting with random people anyway.