I have a feeling that this was a mistake. More details needed, but

He registered to vote on Sunday by using his University of Michigan student identification and documents establishing residency in Ann Arbor, according to Benander.
later contacted the local clerk’s office requesting to get the ballot back, Benander said.

Probably he thought he was voting for the student body president or something similar. Or he thought he was voting in a poll sponsored by the university rather than a real ballot for the real US election (akin to https://deadline.com/2024/10/winner-nickelodeons-kids-pick-the-president-poll-kamala-harris-1236159880/ where kids “vote” but it’s just a poll).

Also,

The student signed a document identifying himself as a U.S. citizen

But maybe he didn’t understand what he was signing due to the language barrier? Maybe he somehow got rushed into signing it (because he was late for class) and only realized what he’d done after he got a chance to read his copy the next day or something?

I’ve heard stories about DMVs just taking your word for it and marking a checkbox. I guess this is different because he actually signed, but even so…

Finally,

later contacted the local clerk’s office requesting to get the ballot back, Benander said.

I.e. he realized his mistake and tried to correct it. Which is was brought this case to everyone’s attention. Guy tries to do the right thing in the end, and ends up arrested.