Citing a "counter-clockwise spin" should clue you in to the intelligence of the person posing this. To actually convey the direction of spin you have to give a specific frame of reference. Imagine a transparent clock. If viewed from behind, through the back of the clock, the hands would be going counter-clockwise.
I would discount the person's explanation of the big bang almost right away. The second question is was matter all spinning in one direction after the big bang. I really doubt this, although this is out of my field of expertise as well. The spin on matter was not imparted until after the big bang when clouds of dust started coming together. Galaxies as a whole have an orientated spin, of course counter/clockwise depends on which side you are observing from. For our solar system, the center of spin was the sun, while minor eddies forming away from the center. These eddies were started by non-uniform gatherings of mass which cause more mass to be attracted to them by gravity. Kind of a snowball effect. The spin of the eddies does not have to be the same as the overall spin of the solar system, although there may be a preference towards secondary eddies spinning the same as the rest of the solar system. Anyway, these secondary eddies resulted in the planets. So planets having opposite spins within a solar system is not against any scientific laws or theories that I know of.
If anyone sees any mistakes, please let me know. Earth science was a while ago and solar system formation was only covered briefly.
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