You're needed over here.

Reading and rereading. I can't see anything the dealer did wrong.
Deposit subject to AA report--report is fine.
"faulty" fuel consumption calced over 4km

lol like someone said "next time take someone with you who knows what the BH they're doing"

Isn't the problem this?
Agreement to buy subject to AA report.
Report fine therefore contract unconditional.
Buyer hasn't settled so therefore seller has to take action to enforce the contract.
Can't resell the car as technically it has sold.
If seller wants to sell to a 3rd party both seller and buyer will have to agree to void their contract.
Logically part of agreeing to void would be the refund of the deposit.
What I don't follow with the deal was why (and even how) did the buyer sign an agreement and pay a deposit on something they had never seen. They then arranged to view on a Sunday (?) and questioned the AA guy about his report after viewing/driving?
Then why did the dealer pull it from TM before the AA report?
I don't see that the dealer has any real reason to not refund the deposit. The dealer hasn't suffered any sort of financial loss, but clearly might if the buyer takes some sort of action to try and recover the $500.

Apart from all of that why didn't the dealer sort out the misunderstanding of the fuel use with the buyer? IMHO it's more a case of potential buyers remorse. Saw the car and then decided she didn't really want it so raised a, probably, nonexistent fuel use issue hoping to be able to back out. Now raising owners -v- age -v- distance as well. Hmmm.

Wonder what the car was? Vitz or a HSV?

They probably were looking at distance to empty