The invoice could be correct and also too high, we are missing all the small details.
What was the duration and distance of the tow. I got mine towed from Grand Canyon village to Flagstaff on a huge trailer with a big rig pulling. 6 hours at 185$ an hour eats a lot in the budget yet in my case I was wise or lucky enough of having an RV CAA card and my cost was zero.
Diagnostic is another story but unless he had some electrical problems the diagnostic portion should be 30 minutes or less, let’s be serious here: check if there is current on the mains of the starter, check solenoid activation (electrical). If there is current and the solenoid gets powered then change the starter..end!
Time for all of this, 2 hours tops.
Price for the starter well this could be high but no more than 600$ for a new one.
So 2 hours at 125$ and hour + 600 + “tow” could equal 1400$, I said could ;-)