Well, for starters, these people need to pick up a dictionary. Blackmail is when you demand money from somebody in return for not revealing compromising information. For example if you demand payment from somebody to not reveal that you found out they were having an affair, or something.
The closest argument could be made for extortion. But even that is a stretch. The argument would be that people like ebayers and craigslist advertisers and so forth that have been using photobucket hotlinking would have to move the images to another host and update their links.
I don't think that is extortion. That's just the end-users being lazy. And at the level where there are so many instances to update that it's a lot of work, why were they using a free image upload service and relying on it for what is effectively a business to begin with?