"Open source" means the SOURCE CODE is OPEN. Which it is.
The internet is full of half-baked "secure" and "private" chat clients and servers. Security is hard to get right. I'm guessing they don't want the reputation of Signal muddled up with some other random client. IIUC anyone can run their own network, and make it as open as they like, using their code, they just can't call it Signal. Much like how Firefox and RedHat use their trademarks.
The internet is full of half-baked "secure" and "private" chat clients and servers. Security is hard to get right. I'm guessing they don't want the reputation of Signal muddled up with some other random client. IIUC anyone can run their own network, and make it as open as they like, using their code, they just can't call it Signal. Much like how Firefox and RedHat use their trademarks.