I cannot reproduce the scenario you described on 8.1. The only think I can tell is that even if you can't see the part in teh parts list you can add it manually to the LHS (left hand side) and the compliance job will accept it.
So I ran into the similar issue as well, and what I found works is the following:
To run compliance rule against Hardware Information.Machine Summary and get the child information for Machine Summary --
"Hardware Information.Machine Summary:/System"
I added the part as follows, by typing in the Property Value of Machine Summary that I want to run compliance against:
To get this in parts:
So the compliance part reads as such:
"Hardware Information.Machine Summary:/System".Model
This is a known issue which is described in the following knowledge article
(You can find it by looking for "No Template parts used in compliance will collect System")
That seems to work!
Thx for the quick help!