The brain is not really rational and neither were the circumstances which created it.
Tinnitus, in many cases, appears to be a result of a handful of neurons in the dorsal cochlear nucleus attempting to keep their output at the same signal strength as usual following an input loss. If we believe evolutionary theory then we may conclude that at some point in the past, organisms which responded to signal loss in this way were more likely to live long enough to breed, than organisms which didn't. Or, even, that the mechanisms which cause tinnitus also have other useful/survival-critical functions in other parts of the orgamisms.
As to the meme -- the brain doesn't really "know" anything. Tinnitus comes from the brain, insofar as it is a neutral and selfless manifestation of a state. Processing that as "sound" and then further deciding that it's "bad" and suffering as a result is an emergent property of consciousness.
This is the best framework I've found through which to approach these ideas without making myself distressed.