SR, I don't think they are talking about the "right" to wear or not wear, but about the "smartness" of the decision to wear or not to wear one.
Personally I didn't use one for quite a while. Felt uncomfortable, eta eta eta... Until the day my saddle broke (without even a hint something is wrong when I saddled), throwing me over the head of my youngster (thank God it was on walk!). That day I realized (yes, I know, silly me to take so long), that unfortunately accidents don't depend on your ability to ride a horse or on how well trained/quiet horse is.
I also want to add that helmets don't protect against everything, but they are handy when you run into the branch on trail or hit your head on something solid when fall off the horse (or together with the horse).