In most places the diesel dispenser is a different size than the gas dispenser to prevent mixups, so you would remember if you had difficulty getting the hose to fit in the tank.
I would try contacting the gas station to see if they can generate a receipt copy or if they have camera footage which would show which hose you used. And I would send a letter to Advantage saying you will not pay the invoice and any legal action they take against you will be defended and met with counteraction. And be prepared to actually follow through on that.