The name is what their reputation is staked on, and if a third party compiled it they have no idea if malware is secretly packaged in there too.
Having said that, the smart move is to dedicate a few engineer hours to packaging it for every linux distribution and every app store, even the smallish ones, to prevent others trying to 'be helpful' and requiring you to send a takedown.
>we really don't want forked versions of the app maintained by other parties connecting to our servers.
that's just misleading misdirection.
Firefox have issues with the legal name, that's why the source is called by other names and the branding is added later on.
signal ties the branding with the code, so it is impossible to build from the canonical source without triggering the branding issue.
So, in practice, it is a convoluted way to annoy anyone releasing from source. And as we know, actually using open source software without a "distro" is insanity. You cannot trust 1000s devs. you trust the distro, the distro trust 10s of package maintainers, the package maintainers trust 10s of devs. and everyone is happy. I trust f-droid just fine. But i don't trust the person who is publishing every apk on random sites like signal.
Not that I really want to defend Signal (XMPP FTW!), but the legal threats were about using the Signal name, not making an unofficial client per se. I know a bit about it because I develop an alternative signal client (a signal-XMPP gateway to be more accurate). That said, they don't help 3rd party client devs at all.