Symptoms
Toyota's consequence line is short: "a battery short circuit increases the risk of a fire." NHTSA's investigation put it more fully — the terminal shorting to the hold-down frame "may result in the sudden loss of electrical power, vehicle stalling, and/or a fire originating in the engine compartment." There may be no warning at all beforehand.
Likely cause
Stated plainly in the campaign: "certain replacement 12-volt batteries may not fit properly in the battery tray, allowing the battery to move and contact the hold-down bracket, possibly causing a short circuit." The car left the factory correct. What changed is that a smaller-cased replacement battery does not fill the tray, so the clamp no longer holds it still.
How should it be checked?
Run the VIN at nhtsa.gov/recalls. Toyota replaces the battery clamp sub-assembly, the battery tray and the positive terminal cover free of charge, and recalls do not expire. Then look under the bonnet yourself — this is one of the few things on this site you can check in ten seconds without tools, and on a car this age the battery has almost certainly been changed at least once, possibly by someone who never heard of the recall.
How can you check it yourself?
Open the bonnet and take hold of the battery with one hand. It should not move at all. If it rocks, slides, or the clamp is missing, loose or improvised, that is the condition this recall describes. Look for a battery that is visibly smaller than the tray it sits in, and check the positive terminal has its cover.
The question to ask the shop
Has recall 23V-734 been completed on this VIN? When was the battery last replaced, by whom, and was the clamp and tray hardware replaced at the same time?