I asked about self-hosted relays on the forum [1]. Right now it doesn't look like they have plans to open the source code behind the actual service. Not sure if that's a 'no, never', or a 'we didn't think about it', but it would be good to ask on the Pi Forums maybe.
Otherwise... the service uses wayvnc for the Pi server part, and you could replicate the setup with TigerVNC easily enough over local LAN or through a VPN. The Pi Connect service is the hosted backend; not sure what they're using there.
The idea of "free beer" is if I'm giving away free beer at my establishment during an event, there are restrictions around that free beer. I'm not gonna fill up a tanker truck for you, I'm gonna kick you out if you start trying to resell it, I'm gonna cut you off it you've had too much, you can't get any if you're under age, etc, etc, etc.
It's free, but you can't do anything you want with it. Really it's free to drink on my terms - and that's certainly "free", but it's not "freedom" (as in free speech).
The recipe for soda is also open source - anybody can make their own carbonated soft drink. But I think if someone offered you "free soda" it would be pretty clear that they are offering you a specific soda whose recipe you almost certainly don't know, not the umbrella concept of "soda".
"Free soda" and "free beer" are analogous, if that helps.
Or, since it seems to need explaining, the point is that "beer" is not one thing with one recipe and if somebody offers you "free beer" it is pretty obviously a specific kind and batch of beer.
So not free as in Freedom, no source code?