Some clarification on this whole $10K question.
First, the dealer has to report any transaction to the IRS if more than $10,000 in cash is involved. If you go to your bank and make a deposit of more than $10K it will report the transaction. These rules apply when in the course of its trade or business a business receives such an amount. It's all part of the anti-money laundering rules incorporated in the Bank Secrecy Act.
So, in the OP's transaction, the dealer will have to report the receipt of the $20K to the IRS. Not a big deal, just part of doing business in the US.
As for why the OP did not want the cash hitting his bank account, he has his own reasons and does not need to tell us anything. His reasons may be entirely legitimate. Generally, however, folks may not want to deposit cash in an account in their name because they may be trying to avoid creditors, which can include ex-spouses looking for alimony or child support, the IRS, or even a party that has a judgment against the account holder and is trying to collect. Sure it sounds suspicious but it's all just conjecture.