If you didn't trust the teacher. The distributed ledger would prevent them from editing the database of timestamps. But then the question is, if you don't trust the teacher why are you in their class?
This is more about trust between peer groups like students vs students or larger groups like departments vs departments.
Imagine a schoolwide project like a fundraiser. Everyone is selling chocolate bars to fund new uniforms. Whoever donates the most gets to decide which team gets a bonus amount. The proof is money received. The coins are distributed.