So it sounds like they're doing the right thing. They're helping people with mental health issues so I want to believe good privacy practices will continue.
Time will tell. Until then, this sounds like a wonderful project.
[UPDATE] Okay, I just tried the app. The first thing it asks for is your name. Fine. Pseudonym, no problem. The second request is, "I need to send you a code. What's your phone number?"
So much for "we don't know who you are". >:
[SOLUTION/PSA] Use a service like Twilio for signup. For $1 you can pull a random SMS-compatible phone number out of a pool, get your signup code from the Twilio web console, and then release the phone number. Not anonymous but obscured identity, at least.