I think the dealer was being vague on purpose.

Maybe your insurance company can pay because of the accident

 

A service writer at the dealer is essentially a sales person, they don't sell you a new car (yet), they sell you tons of service. The more they sell, the more money they make. That's the nature of the business. You always have the option to say "no".

The numbers they provided you don't look like codes from a scanner, they should have that information if they charged you for the diagnosis, you just have to ask them.

Many times you'll get tons of codes, one ecu telling another ecu there's a problem. So you'll have to know where the codes are pointing you, it's not clear where the problem lies when you get the codes.

 

In Toyota’s Electrical Wiring Diagram (more info) for this model, D13 identifies the electrical connector for the water pump assembly, and terminal number 2 (of five) on that connector is shown as having a green wire, which goes to the engine control module (ECM). As the Repair Manual explains, the green wire goes to the WPI terminal on the ECM, which receives a duty cycle signal from the water pump, reporting its current speed.

Only the dealer could say for sure why they noted that terminal, but from your explanation, perhaps the technician followed a diagnostic procedure (say, for diagnostic trouble code P261B) until reaching the point where it calls for replacing the engine water pump, and checking the signal from the D13-2 terminal would be the next step to confirm the repair.

I suppose a really dishonest mechanic who wanted to sell you a water pump and the labor to install it could have disconnected that wire, to cause the ECM to detect a nonexistent failure and store a trouble code, but it would be quite brazen to do that and then put a hint about it in writing.

For future reference: diagnostic trouble codes are typically the letter B (body), C (chassis), P (powertrain), or U (network), followed by four or six hexadecimal digits, and Toyota part numbers are ten or twelve letters or digits, usually written in xxxxx-yyyyy or xxxxx-yyyyy-zz format.

 

Don't be mad them for charging to install the battery. I'm confident you don't work for free, why should a technician? Each and every repair/diagnosis pays "time" to a technician. So.... don't really know what to tell you besides everyone has to make a living.

JC up there is correct however - you always have the option to decline (ie: saying no). Did you check with your insurance company? It's only a 2013 so I'm assuming you had comprehensive coverage. If Liability only - well then I understand trying to tackle it on your own.

 

If you have a smart phone, you could read your own codes for less than $20. You need a Bluetooth or wifi OBD2 dongle (less than $10), and a $6 app for your phone.