Yes for sure, he needs the sponsor letter from his father. Access to the bank account of the sponsor is not a requirement so that letter from the bank he has can't hurt his application but won't be enough either.
The following is a copy of the financial requirements for DTV:
4. Financial evidence: amount of no less than 500,000 THB OR equivalent amount in foreign currency e.g. bank statements OR sponsorship letter covering living expenses.
Anonymous participant dont have to explain to me. Explain to the embassy. Personally I would increase my chances of approval and spend a few months working first. Anyway up to you, good luck.