I had this problem on two computers. I was able to work around it by using 7zip to extract the files and then winrar to re zip them as a .rar. Then I put that file in the NMM mods folder. Restarted NMM and tried to activate. Worked first try.
WOW. I spent hours and hours trying to figure out why I couldn't install NMCs texture pack - but uninstalling 7zip and making WinRAR the default opener for those kinds of files was what FINALLY allowed me to install them. How were you able to figure this out?? I was trying so many other weird, complicated fixes, I mean HOURS and HOURS of trying to other stuff to fix it