However, the issue persisted on a couple of sites within the site collection, even though the site collection at large was fixed. The only commonality with the sites that were still having problems was that I had used Metalogix Migration tool to copy the entire site over to the new environment from SharePoint 2007 to 2010. Most of the other sites, I used the tool to copy data (i.e. lists and libraries), but not the entire site. I had setup the site on the new environment and copied information into it.
After a lot of frustrating poking around, I noticed this within permission levels for the site: