Yes a helmet can protect a person from TBI, but it cannot prevent concussions. The inner rotation impact is what causes concussions for people in most head on collision. Rotation impact is the brain and skull colliding. Even though it looks harmless from the outside with head on collision, the brain inside is smacking into the skull. This is the part that causes concussions. Football is one example of concussion, with head on collision and foreseen concussion on fields. Aside from football, any other activity can cause a concussion. Playing soccer and getting hit in the head by a ball can cause concussion. The same goes with falling off a bike or getting into fights.
Like the TED video, concussion can occur with any activity. Football is not the only sport or activity that is known for causing concussion. Anything can cause head injuries and a helmet cannot prevent those concussion from occurring. Understand that safety is first and that head protection is vital, but still be cautious on any given activities.