This should be completely believable for a company that relies heavily on user and community trust.
That said, @wcathcart: in community with deep technical expertise like Hacker News, folks do consider how many possible channels and means there are to confidentially leak information from applications.
You're correct that in the general case it's likely that tech-savvy users would scan a popular app like yours and find any 'obviously-placed' backdoors. It's an observational and opportunistic approach, akin to the way a passer-by might spot a poorly locked bicycle on a street.
Unfortunately there's an extra level of complexity here - any app may have unusual behaviors that a sophisticated attacker could trigger for individual users to exploit them - and it's really, really hard for the security-conscious of us -- who might never see or meet those users -- to truly trust that your app is doing what you tell us it is, whether that's end-to-end encryption in all situations, or anything else.
The reason is that without being able to see how the app is written, verify that it's genuinely the same compiled version running on all devices, and audit the behavior it will have under exceptional circumstances -- external observers just don't know.
I'm not expecting you to make the source freely available, incredible though that would be - but attempting to explain the potential disconnect in dialogue you might find with some commentors.