A crypto currency is not software.  It is a protocol, written on paper, that anyone can implement in software.  Usually, the guy (or girl) writing the paper also puts some working software up, but that is secondary.  You don't need the software.  You only need the paper of the protocol. Then you can write your own software to use it.

Look at this guy, using bitcoin without running software from somewhere:
http://www.righto.com/2014/02/bitcoins-hard-way-using-raw-bitcoin.html

You don't need core or BU or whatever software.  You can do it the hard way, using some python scripts and a command line interface.  You only need the detailed protocol description.

The use of Pythagoras' theorem is permissionless.  Anyone can use it.  The same for an open crypto currency protocol.  It is nothing more than a more involved kind of statement.  From the moment that you can read it and understand it, you can use it.

In the end, the "permission" is in the intelligence needed to understand it and code it, but again, you are stretching the notion to make it meaningless.