I've encountered a few issues like this. Enhanced Steam uses the storefront API to determine if you own something or not. So if the API says you don't own it, and it doesn't show up in the storefront with the typical "green banner", there is know way for Enhanced Steam to know if you own it or not.
Typically when people ask, I tell them their best bet is either to a) ignore it or b) put in a support ticket with Steam.
And speaking of Enhanced Steam: I've got a few updates I'm working on for the next version, and I'm working concurrently to bring these new features to Firefox. So a new Chrome AND Firefox version are in the works and should be released soon.