The problem I see with not having an agreement is when the buyer shows up
with his certified funds after having paid for a pre-buy inspection, and
finds out you just sold the plane to someone else.

That's true, especially if you allow the owner to see the pre-buy such
that he can show it to other buyers. I've bought a couple airplanes but
never had a good idea of when the best time to finalize price is. There
are two very good arguments. One says you want to agree on a general
price before the pre-buy to ensure you are in the same ballpark before
you spend money on a pre-buy (a factory service pre-buy in a Mooney is
almost $3000). The other school of thought is that its better to wait
until after the pre-buy so you can fully negotiate with the knowledge
of the pre-buy without sounding like you are nickle and diming the
owner down on the purchase price because of pre-buy items that are not
airworthiness issuse, but things that you don't care for (often more
cosmetic in nature).

-Robert