" I used their images/video to make a point. I can see how the video could fall under Fair Use"
Frankly I don't see at all how that would fall under Fair Use, and The Times is absolutely right to C&D him.
Also, "A statement of fact about a company is not a copyright infringement."
No, but a statement of fact about a company that is not backed by public data is slander. NYT doesn't even claim that the reference is copyright infringement, the author just assumes that.
edit: ok, I actually thought he had put a demo website online in which he used the images, so it would look like the NYT's page (but with lorem ipsum for text or something) but he just made an educational video of it, I can see that could be fair use. So I retract my absolute statement. (as should be done with absolute statements in general! (absolutely)) I still think the 'hundreds of hours' remark isn't cool, but perhaps the law is on his side there too.