Underground Strongholds

One of the PCs in my campaign (not a Dwarf) wants to build a sanctum that is partially undergorund (specifically, carved into a mountain). To begin with, I thought this might not be allowed becasue of how the rules for creating a dungeon are worded, but the more I thought about it, the more I thought it seemed like a reasonable thing to do.

Should non-Dwarf characters be able to construct partially-underground strongholds, so long as the distinction between a stronghold and a dungeon is clear?

I think so. History is rich with rock-carved construction by mankind.