They're not even using the Android sharing system. The only way to share from the Instagram app is to upload to Instagram, and optionally tell it to forward the photo to one or more of the sites they support (Facebook, Twitter, Foursquare, Tumblr). If you want real Android sharing, you have to switch to the Gallery and share from there.
It's very annoying: I kept looking for the Android 'Share' button and eventually realized that it just didn't exist on Instagram.
To be fair, Readability is doing a good job of responding to feedback from Android users. There are still more than a few issues (e.g. better control of background processing), but they did quickly turn around support for Share Intents (first out and then in) so I'd say they're moving in the right direction.
From what I understand, they rewrote it from scratch.
They didn't adapt Android user interface guidelines. Example, menu and search buttons are useless; not using share intents, etc..