Yep, there should be plenty of versions, although it could be a rare version, it certainly wouldn't "complete" any other versions of the toys with its own Woody's. Even more, if this toy is so unique (there is no other like this one, right?), it doesn't even complete the full sets of toys available. So, the Japanese museum wouldn't be so strict about having this particular toy. And, why on earth would they destroy all the other dolls?
For me, this all sounds too much stilted. I don't know the video's guy, but I am even skeptical about the veracity of the story. For that reason, I am too very interested hearing a Pixar's official statement. If I recall correctly, the reason why Andy's dad wasn't in the movie was due to the difficulty back then in CGI humans.