I've looked into this further and it seems that this story was distorted.
doinkies searched a little, and found
this blog entry (in Japanese) about it. Basically, what the entry says is that Kawakami Maiko went on an afternoon talk show called Gokigenyou a week ago or so, and she said that it was a friend of hers who wanted a poodle and ended up getting tricked by a website that made sheep up to look like poodles. Not Maiko herself, but a
friend. And doinkies has no idea where these "thousands" of other people came from either. They don't quote anyone else who was fooled, nor do they quote the channel that airs Gokigenyou...if thousands of people had found out they were tricked after watching that episode and called into the channel about it, I'm sure that the people running the channel would have something to say about that.
Also, aside from a couple other blog entries about the episode, doinkies has not seen any mention of this in Japanese news. If some weird scam like this was happening on such a large scale, doinkies is sure the Japanese news would report on it too. Also, why would they need to import sheep into Hokkaido when I've heard there are already lots of sheep farms there? This seems like an urban legend/rumor to doinkies...for all I know there could be such a scam but it's certainly not on the large scale that this article makes it out to be. I think The Sun just wanted a weird story to tell, to capitalize on the "Those wacky Japanese!" stereotypes...
As the Japanese blogger linked above says, "It's uncertain whether or not this story is true, but if it is, this person is quite the idiot." Many of the comments on the blog are of the same type as the comments here, basically "Somebody thought a sheep was a poodle? What a doink!".