Yes as the post below explains in better detail.. the oxygen level has not dropped below the level to sustain life - this type of over simplification could lead someone to suspect that a BO is fatal. A better explanation is that the oxygen tension is so low that the body shuts down a portion of the brain and consciousness is lost.
The brain (or the body) is not harmed by this process, and it is thought to be a mechanism to "protect" the brain and conserve oxygen levels. So the BO occurs when the oxygen pressure is too low to keep the diver awake and functioning.
If an oxygen supply is not quickly provided after a BO, then death will come soon.. It may seem to be a minor distinction, but a high percentage of freedivers have had a BO and the ones that survive are typically not harmed by the occurrence.