But the reason I bring this up is that it annoys me to hear other teachers assume that the former teacher didn't bother to teach rhythm. Or didn't teach it properly.
The student comes in, plays incorrectly. I ask them to count that section for me. They look at me in horror. "I don't like to count."
So your student doesn't count because they don't like to? It looks like you have a defiant student, not one who "just doesn't seem to get it". Your student's problem is behavior, rather than comprehension of the concept.
As for defiant students, luckily, I have never had this situation. The students I have who don't want to count, are actually nice students. They just don't want to follow all the instructions. And their parents complicate matters but praising them and not realizing they are not playing properly. so they come in to play for me not realizing their rhythm is wrong.
I am not a teacher but I would try giving him boogie, rag, swing and stride pieces. These idioms are meaningless without perception of a beat, and might more or less force the issue, given time, provided he enjoys the music.