This is total crap. TL;DR;

1. When doing multiple things at once performance is reduced in each of those things (thank you capt. Obvious).

2. Doing multiple things at once in a specific setting correlates with reduced activity in some brain areas. Casuality not demonstrated either way. No demonstrated relationship between "brain damage" and lower activity, so the claim in the title is at least two logical errors away from the raw data.

3. Buy this new book about EQ (which is pseudoscientific crap on its own).