I'm not sure what you mean. They were using a tool that encrypted their communications, it just wasn't good. What's the difference between using Signal and using what they were using, or using GPG and what they were using?
The difference is the action of encryption and decryption is completely transparent to the user in the case of Signal or this thing they used. You don't encrypt anything, you input plain text and then the system takes over and you have to trust it. If the rumors are true the authorities compromised the servers, pushed an update to the app and the encryption no longer happened.
Just one example on how to do it yourself: using PGP you can use any hardware (not a phone marketed to criminals) and keep it completely offline. And use a phone (worst option but whatever) in which you input the encrypted thing directly. So you don't have to trust the network device. Bonus: neither do you have to use something that makes you stand out to authorities.
"Don't rely on others" makes no sense for encryption, you have to rely on others because it's too hard otherwise. You just have to pick trustworthy others.
Moxie going on twitter to say the cops have broken into Signal would be headline news, at least in the tech world.
Do you really have the talent in your organisation to develop a better cipher than AES or ChaCha? If not, go with something that exists. According to Snowden, even the NSA can't just break PGP if you use it properly.
Do you have better coders than OpenWhisperSystems? You're going to have to trade off relying on someone else's software versus the chance your own coders make a mistake. I'd say the latter risk is usually the bigger one - even the Sony PS developers messed up on the "don't reuse nonces" bit.
Do you have your own chip fab? If not, you're going to have to hope whatever you're using doesn't have too many backdoors.