I have been staying with ICH for 5+ years now steadily and always on Gov't rates. I do have the ICH version of the Gov't traveller card along with my Government contractor ID. I have only 3 times ever been asked to produce
any form of Gov't ID.

So I don't know, I guess YMMV.
I also always use Gov't for my leisure stays as well and have never had a problem.
Have you told the hotels that you are not on official government business and that this is leisure travel? I didn't say that individuals don't get the rate. I stated that members might not be getting it legally, according to the rules. Some employers would frown upon this. I know that I have asked several hotels if it were permissible and their response was - "No, you must be on official government business."
mxm135