The fear is of the radiation. Telling people that there is none remaining in the treated food does not dispell that.
A century or so ago, radiation was "the" latest thing in medical advances, and was used for all kinds of things, some of them really weird and alternative.
Then came the realisation that it could have strange effects on the body, and then eventually came the bombs on Japan, with their terrible results and after-effects, and it became a bogeyman, killing maiming and distorting invisibly.
When food is irradiated for a longer shelf life, the radiation passes through, doing its job, and is gone before the food is on sale, but many people are still subconsciously remembering what that radiation could do, so they fear the food which has been treated with it. Hence all the jokes about glowing in the dark after eating radiated strawberries.