Whenever I install a theme from WPMU DEV Dashboard, all runs fine.
However, plugin installations do display an error related to folder permissions. I can assure you this is not the problem (the server is self managed).
I have tried even a LogLevel debug in my Apache to backtrace and nothing interesting appears in Apache error log while I do try a plugin installation.
Can you please update the Dashboard, including a verbose output (or log) of what is being done during the plugin installation (like "doing this > ok > now doing this > ok > and now doing this > oops, failed!") so we can detect where the issue is?
I have found various other threads with the same issue. I expect the verbose output help us resolve this in a definitive manner.