Hmm.. I think you're right on that point. I do have one that does, but probably most do not. Benchtop instruments like my Agilent 34401A meters do have an "infinite impedance" setting.
1M? What a POS. What do you expect for dollar store prices. Even the Chinese can't make a worthwhile meter for what Harbor Fright wants to pay.Carbon? AFAIK something like Ruthenium oxide is more common in chip resistors. Ohmcraft makes their using a kind of printing method which is automated, so it should be consistent. Here is a white paper on their process: