I believe that I can explain the problem a little more concisely. Please feel free to correct me if I've misunderstood the inner workings of Joomla.
A typical Joomla article URLs would require some parameters:
* Itemid - the ID of the menu item to use
* catid - the ID of the category
* id - The ID of the article
* lang - the two letter sef code for the language
So a typical NON SEF URL might look like this:
Internally, Joomla always uses this URL. Typically we would use the JRoute method to pass these URL and create a SEF URL. When you use the SEF functions, then it's making the URL pretty, but still passing Joomla the same information.
So if you have a URL that looks like this: http://www.example.com/en/menu/456-cate ... ticle-Name
Then it's really just grabbing the parameters (looking up Itemid from /menu/, lang=en, catid=456, id=789) and passing them to Joomla, then dumping the other stuff.
So really you could pass the a fake or incorrect URL like this and it would work the same to Joomla. http://www.example.com/en/othermenu/456 ... ticle-name
In other words, Joomla doesn't care what the words say as long a it can get the ID parameters out of the URL. So anyone in this thread that's reporting that they passed a different URL name to a page that shouldn't exist and it comes up... thats just how it works. More importantly, that's how it's supposed to work. So anyone above that reported that error... sorry. I think you're SOL.
The real problem (IMHO) is that Googlebot is somehow indexing pages that shouldn't exist for links that were never created.
So in the bottom example: http://www.example.com/en/othermenu/456 ... ticle-name
The problem is that these articles all exist in /menu/, but for whatever reason are also showing up in /othermenu/ - but we don't know why. Because of the way Joomla SEF works, these are seen as valid links and are rendered - only the page is being shown with the wrong menu item (with the wrong modules and wrong template).
In looking through every page of my site, I cannot ever find a link to these items, yet they are showing up in Google webmaster tools as being indexed. I personally believe that it's a problem with the category blogs with linked titles turned on. It's somehow finding and linking all articles under a category that they shouldn't be in.
Let's keep thinking about it and digging and we'll come up with solution!