I'm not sure what's going on here. The only time I've seen or heard of a message like that is if you have a specific iOS app for your site or product. If so, you can include some meta tags on the page which let Facebook know that the user could have an improved experience by logging in directly through *your* app, not necessarily the Facebook App itself. I think you can also add app details to your Facebook Application, which will also let Facebook know there's an alternative method.
I know you've discussed having your own app in the past. If so, that's my guess as to what's happening.
Let me know your thoughts,
Alex
Facebook login - not seeing app on mobile
