Its Bear, and even in the US, minors do not have that right. The right belongs to the parent. That being said, while it may be legal to own and even to discharge a marker, if it were to be classified in the same category as a firearm (which should never come to be), they would be constrained by the same laws governing the discharging of the marker within a distance of a roadway, building, or unwilling persons etc. So while the constitution may protect the right to own them, it is possible, though not likely, that laws could be passed to make using them illegal.
Strangeglove, your absolutely right, and few things piss me off more than getting owned by guys 3,4,5 years younger than me. What people mean though isn't the experienced younger players, its the 12/13 year olds who want to try paintball for the first time. Until they've lived the game a little while, people don't understand how dangerous it is.