If LR can open a file from a camera, that camera is supported.
The naming convention Adobe uses sometimes leads to misunderstandings. The 'standard' profile you are using is the one specifically created for the 5D3. When LR detects a file from [e.g.] a 10D it will also show 'Adobe Standard' as the profile, but it is actually a different profile.
I've checked, and for the 5D3 the 6 usual standard, faithful, etc are available.
They reside in the programme folder of LR, if you want to check search for '5d Mark III'