I don't think the wiring diagrams would have told them much.
The question is, why is the ECU instructing a low voltage to the seat heaters - if true, it makes no sense. My understanding is that the canbus shuts down seat heating completely in the event that it detects low voltage at start-up, but IIRC should then throw a warning symbol on the dash - I assume this is not present?
Keeping things simple, I have to see the battery as first suspect though. 12 volts standing, if correct, is a low reading; it should be showing around 12.6v. If you have a multi-meter, set it up to read battery voltage across the terminals - switch on the ignition & see what shows when the canbus checks out & the fuel pump runs up. Then, once settled, press the start button & see how far the voltage dips as she starts - my suspicion is that you will be looking at a significant drop. I can't recall the threshold for achieving a start off hand, but if you check back here doubtless someone can interject.
Alternatively, if you don't have a meter, why not get a battery specialist to check your battery quality. It could save you a long ride.