He has it half right, from what I understand.
As overall temperature heats up, colder water finds its way into the gulf stream. Which may eventually result in a redirection or cessation of the stream. It's thermodynamics in action, like.
And if that happens things further from the equator will cool down considerably, on account of the stream acting as some sort of conduit for warmth.
Whether or not we have had a significant impact on the process thus far is debateable, I wouldn't buy this documentary you are citing wholesale any more than I'd trust Gore's completely.
What I think is pretty much certain is that our polluting only can have a negative effect, it's the scope of it people can argue about (might be microscopic, might be considerable), and I really think we should take heed of the warnings for that alone.
EDit: And for the record, I've watched neither of the documentaries in full, but they both seem like propaganda, and somewhat weak in the facts-department.
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