Comment 14 for bug 56880

I own my thanks to David Robert Lewis at #12. After executing

sudo dpkg-reconfigure --force msttcorefonts

the interactive interface (I'm not sure if it's graphical yet) guides well, including asking for a customized mirror. Since I found the problem is with the default mirror of my country is not working (changing to another mirror on Sourceforge.net enables downloading well), I have found that typing a custom mirror may bring the font installer to life, for example:
http://nchc.dl.sourceforge.net/project/corefonts/the%20fonts/final/

Then msttcorefonts installer will be able to locate the files, and extracts and installs well.

So I figure that such bugs (there has been a whole bunch around this package on Launchpad...) may be related to proxy settings, but may also be due to invalid Sourceforge mirror (frustrating...). So, just change to another valid mirror. Guys, why not give it a try.