This is a pedicab service. A cynic would assume that Pedal Me is mandating this (and thus putting their drivers at risk) because passengers are more nervous about taking a service where the driver wears a helmet and they do not.
This might lower risk for the customers because driver may take less risk without a helmet in some situation but the risk for driver is only increased.
This is optimizing for customers at the cost of drivers.
I don't see any supportive extensive research linked from them .
I suppose it's also not reasonable to provide seatbelts to passengers as well as the driver of a taxi?
No. Which means it's not automatically "the reasonable thing", just an opinion.
So I'm curious what the REASONING is behind your feeling that offering passengers the option to wear a helmet is unreasonable. Personally, I would AGREE that offering passengers on a pedicab the option of a pineapple would be unreasonable. There just isn't any practical correlation between pineapples and pedicabs. But helmets are different: there are large numbers of people who campaign vigorously to persuade others to wear helmets when on a bike; many places even have laws mandating helmets on bikes, at least for some ages. So it is a plausible thing for passengers to want. Given that, why would it be unreasonable to offer it?
I'd worry about lice.
Also, the idea is to offer an option. Not to make it mandatory unless legislation require it. If your passengers are more comfortable not wearing them, their choice.