Even in your "reference article" it it said: "The actual amount of radioactivity is extremely low -less than the normal background radiation you get from rocks and stuff" and "if in fact it's a problem, is that uranium is a heavy metal, as is lead [;]both could leach into food, particularly if it's acidic."
So if you really wonder the risk for your health, don't measure it with a radiometer ! (any kind of heavy metal, in particular any isotope of uranium, is then the issue, while only some kind is radioactive).
Further, in physics as in biology, quantities is a key thing. If you extract 100% of the paint of a plate in order to eat it all, how much nanograms of heavy metal it makes ? which proportion would be absorbed by your intestine ? Compare to the recommendation thresholds.
Then, in physics as in biology, comparisons and proportion is also a key thing. Among all the risks you have around you, even just those related to food and eating, what would be the order of importance of this one in the ordered list ? When was your fridge disinfected for the last time ? How fresh and isolated was the food ? How rinsed were the dishes ? (and are you sure of the metal of the spoon ? or the air of the room ?).
In term of food-related risk it seems that many fantasy or true but very small things are in focus, while people seems to have totally forgotten that our very first historical enemy are bacteria (more bleach everywhere, please. And avoiding uncooked and cooked chicken sharing a same plate in a row is probably way more important than the paint below).