I would have pointed out that 'muppet' is a trademarked name, and Disney is fond of suing people for copyright infringement. Most people don't realise it's copyrighted, nor that there's a difference. Frankly I find most people on the net also don't care about copyrights.
I do think we have a right to ask for the correct language to be used; especially because in this case, it's about the law.
More importantly though, when writing for the general public, most people don't know much about puppetry and the various nuances. I'd say that there is something kind of correct about not wanting to confuse an audience with complicated terminology that require long explanations unless it's absolutely central to the point of the article. We can nitpick about whether or not a shadow puppet can better be described as a rod puppet; but a passing person who wants to know about a cool new video won't care nor take the time to understand.
I also wrote an article about the difference between a 'muppet' and a 'puppet'.
http://www.schoolofpuppetry.com.au/tutorials.php/what-s-the-difference-between-a-muppet-and-a-puppetInterestingly, I think most of it is to do with the fact that it requires education of people who blog or journalists. There's a science/entertainment exchange which tries to get artists working with scientists in order to get more accurate science (or reality) depictions into artworks.
http://blog.scienceandentertainmentexchange.org/I think it's no different than with puppetry: we just need to educate as much as possible and hope eventually people understand more than the 'puppets = muppets' myth. Additionally, puppeteers actually get sucked into the trap because of the general public: if someone searches for 'muppet' you want them to find your product/site, and so puppeteers/toy makers tend to label their wares according to myth rather than according to fact.
A last word: I had someone leave a comment on my site that you can see at the above article. They called a muppet something I'd never heard before, and so replied via email asking them to elucidate on where they heard it or why they believed it was a correct term used by actual puppeteers. They basically wrote back that they read it on some website - no URL or name provided - and that I couldn't change their minds about it.
Fact is, some people just assume that every website has trustworthy info on it and there's no getting around some of the myths out there regurgitated and unchecked from a reliable source. And the only crank in the room is the one who isn't willing to accept new info from a person who has actually studied the subject in detail.
@VW... I've had similar experiences.
@Cruppetman, Speaking of unusual terms, Nana Projects uses shadow puppets and call themselves 'lanterneers'. I always liked that.