While you are almost certainly right, the problem lies with the fact that Toyota is famous for almost always refusing to do any modifications to the wiring or to connect anything to the wiring that is not a Toyota part because "it would void the warranty!" As you said, that is the party line and most dealer service departments stick to it, regardless of truth, logic, scientific evidence notwithstanding. The main problem is that if they want to deny your coverage because of some minor modification, eventually the only way you can fight them is in court and that means you have to go hire an expert witness to testify that it didn't do anything to cause the failure and they don't have to hire anyone because they have hundreds of engineers on staff, many of whom go to court every day to testify in other product liability cases. It is an almost insurmountable obstacle for a private person. A plaintiffs lawyer might be able to have a couple of experts under contract to counter this, but they don't come cheap and they aren't going to be cost effective in a case for a few hundred dollars of lost warranty coverage. Or even a few thousand dollars.
I tried to get them to give me a switched wire and ground wire to hook up my radar detector on my Prius (I know, delusions of grandeur and a total waste of time and money) and they refused. I did it myself because I knew I could reach in there and pull off those two wires any time I had an electrical problem (if I did) and show up at the dealership with no modification. I am not sure I would want to be taking a ballast and HID on and off. Just my thoughts.