After a two hours on the phone with Apple Care, a senior advisor recommended that I reset my phone fresh which would have erased my text messages and more. Needless to say I didn't follow his advice and figured the following out on my own. The resources that I was trying to access was Mad Men episodes that I had purchased from the iTunes store. I don't know what you were trying to access so your mileage may vary.
I can't say with 100% certainty since I don't remember if the downloads completed successfully to my iPhone but I suspect that they didn't. I deleted all the video content that was syncing from my iTunes library on my Mac yet I still had the four pieces of content listed in the Video app even though the Video app wasn't even listed in the storage usage in the iPhone's settings.
So essentially, I believe that the iOS iTunes app reports that content has been downloaded to the device at the beginning of the download and the Video and Music apps see the metadata of the content. However, since the content itself hasn't been successfully downloaded you get the "You don't have permission to access the requested resource." simply because the file doesn't exist on the phone.
To correct the issue, determine which pieces of content that you are issues with and redownload them from the purchases section of the iOS iTunes app. For videos, it didn't matter if it was HD or SD format. You can then view the videos or delete them with a side swipe, which I couldn't do before the redownload.
Hope this works for you.
So I am sure the steps are probably the best thing to try in the long run but for a short term fix, if you click videos, then click shared and the "My iPhone" will be ticked. If you click your library, let your phone do its magic and then et viola, you should be able to view your videos.
This worked for me
Let me know how it goes.