MTV says it is. DirecTV broadcasts the HD signal they are given. That there is a 4:3 image in the center of it instead of a 16:9 image is MTV's issue, not DirecTV's.
You won't find anything that says Nick is HD also, but it has shown HD programing.
Take your issues to VIACOM not Directv. Let Viacom decide what to do with MHD
The channel arrives at your receiver as a 1080i stream. That is an HD stream. You may not like the fact that it is a 4:3 upconverted SD image turned into a 1080i stream, but it is still an HD stream.
Send the complaints to Viacom, who owns MTV. DirecTV is getting the channel to you. Any problem with the content should be addressed with the owners of the channel.