I think it's a ridiculous statement which the author (I mean the person who first said it) has absolutely no grounds to back it up on!
The biggest thing is that NOONE KNOWS or even comes CLOSE TO KNOWING how many atoms are in the universe!
a) The universe is 'mainly empty space' - Granted, but there are many debates about what this empty space actually is, i.e. the Dark matter debate, and does that somehow contains some kind of atom?!?
b) We have no idea how large the universe is...
b I) IF the universe is infinite in size, then the statement is clearly false.
b II) It may well be infinite, it may well not, but the vast ridiculously large and incomprehendible size of the universe means that it cannot even be accounted for by humanity, we just don't know enough about it, or have any clue as the the size or extent.
c) ALL of our knowledge so far about the size of the universe is based on PURE conjecture, there is no unifying theory of its size or origin, or even the very nature or what is happening.
d) We DO NOT know if the universe is expanding, stable or shrinking, thus possibily changing the 'number' atoms constantly.
e) ANYONE who claims that they do know the size of the universe, or what is happening to it, is in a small minorty and will be contested by many many scientists of many many different levels.
f) any such claims such as above like "Unless you live outside of the universe" are impossible and equally ridiculous. By its very definition, the universe contains everything, there is no 'outisde the universe' to live, as everything in existence is part of it.
Short answer: Whoever you heard make that claim was talking rubbish, and obviously was just trying to make the point that there is an incredible number of possible connections in the brain. Such exravagent claims though, only undermine his position. Furthermore he is obviously a Neuroscientist of some ilk, and knows nothing about astrophysics.