#2 and 3 don’t actually happen since it can’t be recorded on the P&L.
The donation would get recorded to cash and offset to a liability account, probably something named Charitable Donations Payable likely with a subaccount for the specific programs.
Overall, the effect is essentially the same, though. Fwiw, I like to use the same comparison as you did to show to people how dumb this belief is.
The individual who donated at the register also is allowed to claim the donation when they file their taxes.