Aren't both the "move to another location" and "pass on a sickness" meanings of うつる represented with 移る? As noted in the definition, usually the "pass on a sickness" meaning is written in kana, but that doesn't make this incorrect. Just less common.
Here's a monolingual dictionary entry (meaning #5) showing that the "pass on a sickness" meaning is associated with this kanji.
https://www.weblio.jp/content/%E7%A7%BB%E3%82%8B
Again, that doesn't mean most people would write it this way, but I would say your coworker is a bit overzealous in deeming it "incorrect" rather than "unnatural" or "less common."
And sorry for the triple post, but I think the most natural way to write this would be バカがうつる, which no kanji for either バカ or うつる.
Again, that doesn't make the representation in the sentence above "incorrect" though.
The actual issue with this sentence is that the furigana are incorrect. It should be:
馬鹿(ばか)が移(うつ)る
Mistaken kanji
While searching for examples of 移る, I found this sentence (as it stands, it is the first example that appears in a search) and thought the kanji usage to be unusual. It sounds like this sentence has confused うつる with the version that means to pass on a sickness, not to move to another location. I asked my Japanese co-worker, and they confirmed this kanji usage to be incorrect.