It would be prudent in this situation if you could directly talk to the teacher concerned, and explain this problem to them.
I agree that this is something that the child is exacerbating ... however this is precisely the reason why the teacher needs to intervene in a positive manner.
Maybe giving him some responsibility can help, something that engenders trust in the child.
One positive thing that helps in this situation is that the child is made the 'monitor' for a particular row of seats. His job profile is to put the chairs in proper position, pick up the sheets after any work is done etc.
The child is clearly conveyed (by both you and the teacher) that this is a serious responsibility and the teacher looks up to them to stand as a positive example to the rest of the class.
You can discuss these approaches with the teacher, and hopefully things will get better soon :)