I think you have that backwards, WebRTC doesn't work, and STUN does.

I think you have it sideways. STUN [1] is the NAT traversal / "NAT hole punching" process that allows peers to discover their public IP addresses and establish direct P2P bidirectional UDP communication. WebRTC depends on STUN to establish P2P communication. You may be thinking of TURN [2] which amounts to routing traffic through an intermediary node that is visible to the two peers.

[1] https://en.wikipedia.org/wiki/STUN

[2] https://en.wikipedia.org/wiki/Traversal_Using_Relays_around_...