Although the screen resolution isn't up to 1080p, the iPhone (3GS, 4, 4S), iPod touch (> 2nd Gen) and iPad are all capable of decoding 1080p content (as long as the profile isn't too high). I know this because whenever I use Handbrake to rip a bluray at 1080p, it works fine on all of my devices. iTunes will even stream them over home sharing.
However, all of this falls down if you flag a video file as HD 1080p. I found that when I was opening my rips with Subler (to add artwork and metadata), they would no longer be visible in my shared library via my iDevices, only AppleTV 3. This was happening because Subler was setting the HD flag to 1080p. I found that changing this in Subler to 720p or None, resulted in the rips re-appearing in the library.
So, this is not a device limitation, it is iTunes being restrictive. iTunes shouldn't restrict based on video resolution, it should restrict on the encoding profile.
I've never tried opening a purchased movie with Subler but, if you can, try re-flagging your content as 720p and see if you can now sync your 1080p content. Don't worry, it's only a metadata flag that you're changing, it won't change the resolution of the movie.