Untrue. He only wants distribution through channels that provide the same security assurances and deployment features that Google does through the Play Store. [0][1][2]
He's also quite open to replacing use of GCM with WebSockets or some equivalent tech, but if you don't use GCM, the replacement is likely going to significantly reduce battery life of phones on cell networks. [3][4]
> ...and even went as far to demand that free/libre Play-alternative F-droid removed their build of TextSecure.
That's because -in part- the F-droid project managers had (and -AFAIK, but I haven't checked in quite some time- continues to have) very serious issues in regards to their APK signing key handling procedures.
Signal is GPL'd. Anyone can take the code and do what they like with it, as long as it conforms with the license terms. However, it's very clear that Whisper Systems does not want people distributing Signal-branded builds on app distribution platforms that don't provide Whisper Systems the security guarantees and management tools that they need to get their jobs done.
In short, you're free to distribute custom builds of the Signal-Android, Signal-Desktop, TextSecure-Server, and Signal-iOS projects. However, it'd be nice of you to:
* Stand up an instance of the Signal server software on hardware you control, then point your builds of the Signal client software to your server.
* Rename the software that you're redistributing, make up your own logo, and make it abundantly clear that -while your work is based entirely on Signal's code- you're neither operating with the explicit support of Open Whisper Systems nor are you likely to be providing the same security guarantees that they are.
[0] https://github.com/WhisperSystems/Signal-Android/issues/127#...
[1] https://github.com/WhisperSystems/Signal-Android/issues/281#...
[2] https://github.com/WhisperSystems/Signal-Android/issues/127#...
[3] https://github.com/WhisperSystems/Signal-Android/issues/1000...
[4] (see the reply to) https://github.com/WhisperSystems/Signal-Android/issues/127#...