It seems that since the change in the site, ANY video file uploaded to their server is ALSO uploaded to MegaVideo, a streaming video site. This is a big no-no for a lot of people who record shows and especially for fansubbers.
But, there are a few ways to get around this, seeing as MU is still the best deal around for uploading files (seeing as it's unlimited bandwidth and large filesizes for premium users, whereas MF is either limited to 100mb per file OR even with pro a bandwidth limit a month).
When uploading videos to MU, please either change the file extension to ".abc" or zip the file prior to uploading. This will prevent MU from being able to stream the file. To change the file extension, simply rename the file from .avi or .mp4, etc. to .abc. You will more than likely receive a warning that this will make the file unstable. Hit okay and then upload it, making a note as to what the file extension should be for the downloaders. Once the file is uploaded you can change the extension back to whatever it was originally and the video will work. Same for whoever downloads it. I find this to be a much easier way than zipping the file, THEN uploading it, seeing as zipping large things can sometimes take almost as long as uploading them.
As far as I know, this has been brought to MU's attention, but I highly doubt anything will actually be done to stop it.
This is very important considering the recent closure of several prominent Clubboxes due to file sharing issues (though those seem to be limited to the Korean fandom, as far as I can tell?) and issues with fansubbing groups and YouTube/CrunchyRoll/Veoh/MV etc.
If you have any questions, please feel free to ask them here! :)
EDIT: Apparently, there is a way for uploaders to delete the MV streaming version by logging into their MV account (same information as your MU account) and clicking the first "Videos" Link on the main MV page. (My: Profile Videos etc). (This can also be done through MegaManager under the Megavideo tab.)
pinkujisatsu linked to a tutorial on how to delete the MVideo file here.