I am not spreading false information. This is what is said on development updates:
TeamSpeak Development Status Update - #148 by Luuubb clearly tells us TeamSpeak v5 is using Matrix, so that kind of compatibility is possible only in two ways:
*TeamSpeak 5 seamlessly falls back to TeamSpeak 3 protocol when speaking to a TS3 server (this is indeed possible).
*TeamSpeak 3 protocol is a forwards-compatible predecessor of Matrix protocol (which, as we know, is not true).