Your agent is working for you. They know the market better than you. I know this because if you wanted a meaningful answer, you'd have included meaningful details. Like, how big a discount was the $15K? Your agent wants you to close a deal so they can get paid (By the seller), suspected your offer was poor, and was proven correct. They're giving you sound advice.
No, there is no requirement that an offer be rejected in writing. There's nothing saying that it be rejected at all. The seller can just ignore it.
Ease off on the paranoia and conduct a business transaction.