Just to be clear Toyota wheels can be finicky to balance because most people are poorly trained on tire balance machines and easily mismount them when using cones; on top of the large bore size used by Toyota for most of their 6-lug & 5 Lug truck wheels.
The Hawkea "finger" adapter seats the wheel the lug holes so that when mounting on a cone it is flush against the balancer shaft face every time. It is a tool designed to improve accuracy and consistency when balancing the wheels. Can you get by without using it? Sure a lot of dealer techs don't bother with it because they "know better" or just are experienced with balancing wheels; can it cause a comeback if not used? Absolutely, but a more important aspect is doing a proper road-force balance as well. The finger adapter can only go so far, but it does help make typically "difficult" Toyota wheels better balanced (particularly when running heavier tires.) Hence why there's been a TSB out for over a decade on the issue.
Post Note-
I don't normally just outright be an ass to people if they tell me something that sounds stupid. I usually try to let them explain their reasoning before I pass judgement. I have a feeling had you asked them WHY Toyota wheels are finicky to balance, you would have found the explanation satisfactory versus assuming that they are just trying to get one over on you.
This. Failing to make the wheel concentric to the balancer rotational axis will of course give a poor balance. This is true of ANY wheel and tire. It's pretty easy to verify if the wheel is centered by checking runout with a fixed indicator (i.e. piece of metal propped up on balancer), but most tech don't do it from what I've seen and just assume they centered it right.
As for the OP, sounds like a real piece of work...