So, if something costs $100, the buyer's premium brings it up to $113, then the 3% discount drops it to $109.61, right? Not $110.
Heading to an auction tomorrow, expect to spend enough to where the innumeracy makes a difference. Apparently, these are the people who think that if something's on sale for 60% off, and you have a 40% off coupon, that it's free.
A forty basis point delta is going to make a difference? Holy crap, how much are you spending? Just to illustrate, if you spend $10,000 the delta is $39, and the auction house (which is where I assume the buyer's premium is going) makes $1,000 on that.
FWIW, you're totally right. the 3% discount is obviously to offset the merchant's fee on a credit card, and that merchant's fee would be applied to the buyers premium as well as the notional amount of the winning bid. If I was in your shoes I would argue it if it was anything over $1,000. Just bring a calculator and show them.
As an aside, it just occurred to me that they really just want to make $10% on the auction after merchant fees. The real mistake that they're making is that they should be charging a 13.4% buyers fee with a 3% cash discount. So a $100 notional bid would cost the buyer $113.40, subtract the 3% merchant fee (or cash discount) and they're left with $109.98.