I rendered a video in LRT 3 using the 4K setting and it doesn't play right in PR CC. I know there is the warning about older programs not being able to play it properly but I am using the latest version of Premiere.

Any idea why?

I'm on a Mid 2009 MacBook Pro and I attached a screen shot.

Please try a lower quality / frame rate and see if it works.
All my tests with CC were successfull, didn't experience any problems - even with 6K content.

I tried rendering in 3k and didn't have any problems, it's just 4K on all the quality settings from low to ultra high that is having problems.

Although, if I render it in 16x9 the file is playable. It's just the uncropped 4k files that are not working and creating an error.

I'm thinking it must be a problem with my Mac. I can't play the file in Quicktime but it plays just fine in VLC.

Does this make sense?

Yes, like I stated, the uncropped 4K MP4 are Level 5.2 that's unsupported by many software products.
An alternative would be ProRes, it's more suited for that high resolutions.