For the record, I am of the mind that "signage is the final arbiter if signage is consistent" and I would thus include any "county" Hawaii routes that are consistently signed. The casual traveler is not going to recognize any difference because it's exactly the same shield design, and if these routes are omitted this is only going to keep coming up as one by one people go to Hawaii, see a route signed, then wonder why it isn't in the HB and report it as missing.
Incorrect signage is a common theme. I recall the discussion of I-30Bus in St Helens OR when the sign should have clearly been US30Bus. I can remember a fair number of state routes that used the US numbered route shield. Clearly just the wrong shield being used. Hawaii doesn't have a separate shield used on county routes when they are signed at all.
Parts of county road 180 on the Big Island are signed, but the signage is sporadic at best. It's easy enough to pick out the proper route, but reassurance signage is almost non-existent between HI11 and HI190. 520 and 530 on Kauai are generally easy to clinch, mainly due to signs with the intersections with HI50 and with each other, but still doesn't make them state highways no matter what the signs say.
I'll admit the confusing signage led me to drive a couple county roads I might not have otherwise taken simply because I didn't want to return home to find out I'd missed clinching something. Since HDOT does distinguish between state and county roads (even if the signage does not), that's the distinction TM should take as well. When it comes up in future discussion (as it likely will), @oscar can post quick reply about the state vs. county roads in HI to explain why TM includes one set but not the other.