Your accountant is trying to simplify things, but he is technically
wrong. I think he's just assuming that your record keeping isn't
up to the task, and is looking for the easiest way out, to stay
under the IRS radar.
Whether it's a signer or not doesn't matter - ALL winnings,
any size, are taxable income. If you itemize deductions, you can
also deduct losses, but only up to the extent of your winnings.
But, in order to look reasonable to an auditor, your betting history
would need to show other winnings (surely, your 'signer' wasn't
the ONLY time you won).
You probably won't get audited, anyway. It all depends on the
local office and how many other 'flags' you have.
