You are not wrong about the bullet proof vests. The vest may stop a bullet from puncturing your vitals, but the concussive force of a bullet can still cause damage not unlike being hit with a sledge hammer.
Of course, there's still the matter that no matter how 'invulnerable' you may be, Nerve Endings tend to still function, and pain, by itself, can do a lot of damage. Taking a bullet to the head, for instance - that's got to be even more dire than getting a 'simple' concussion in a sports scrimmage!
(Not that Lena would mind though...)
Birds chirp because all those crude things they say nonstop have to be bleeped out!! 8-O