The company chose to spend a lot of time evaluating all these take home projects, in the first step, and then reject people for silly reason afterwards? It's a lose-lose situation.
Sounds like their hiring procedure is deeply broken.
It may have looked like the applicant had someone else do the take-home assignment for him.
That said, I imagine that they could have interviewed in a more constructive way that may have been less stressful (e.g., walk us through your thought processes as you completed this take home assignment — most frauds can’t do this convincingly).
The company definitely could have done better. If you have someone hitting a home run on a take home assignment, at that point a no-hire decision better have some very strong justification behind it.
Sounds like there are better places to work.
I hope you landed in a good place.