If a cyclist have a helmet he and everyone around him behaves dumber. This was researched.
Less accidents overall? I can believe that, maybe. But you'll need to back up "less severe ones".
If a new driver who's phone distracted them for a split second is going to hit me on my bike, I feel like it's going to be more severe if I don't have a helmet on.
Without the helmet you die on the road. With the helmet you die at the hospital.
This seems like an extraordinary claim, given that safety systems in all other places have no such effects (or at least, not as significant). I would very much like to see this research, and even then I would be very wary of it.
Either way, it's irrelevant given the levels of training that they are claiming they demand of their drivers. Given those claims, it's obvious that they helmets + training would be safer than just the training, if the training is good enough to protect the drivers at all.
There are examples where safety systems cause increased risk.
Football helmets are one. The helmet doesn't protect very well against concussions and the presence of the helmet makes it more likely for players to use their heads as a weapon.
I don't know about this bike helmet example since the actual data isn't available, but there are definitely times when counterintuitively having a safety feature is riskier.