Well, what they are saying is that blood, and its contents, have some direct detrimental effects, but the most immediate, significant damage is due to secondary effects of all the leaking blood. When blood escapes the vessels, it builds up, and causes pressure to increase within the skull, harming the brain. Also, with the controlled flow of the blood interrupted, the brain does not get the oxygen it needs. These are factors secondary to the blood flow no longer being controlled by vessels.

 

The direct effects of disruption of the blood-brain-barrier (neurons exposed to inappropriate stuff/concentrations of stuff, and products of decomposing RBCs) is indeed damaging, but it is the deprivation of oxygen that has the most, lasting effect. The neurons recover from the damaging, but not so lethal, effects created by the presence of blood, but the secondary lack of oxygen, is what kills the neurons.