They don't really have anything to do with each other except that without
content a media center is of little value.
A free software media center would be a little computer with remote that had
no depencies on non-free drivers, firmware, or other software. In other words
users would not need a propritary peice of firmware to do HD decoding or have
access to web sites that dependend on Adobe Flash's digital restrictions
managment capabilities.
I don't know for a fact that sites like Hulu and Amazon Instant Video (the
two big ones that work with GNU/Linux distributions which include or make
installation fairly easy of the Adobe Flash player) are utilizing this
although I haven't been able to access these sites with Trisquel. If I recall
correctly I once heard Amazon was at least initially not doing anything to
restrict content. If that is true then in theory it may work at some point in
the future with Trisquel and other free operating systems. I'm not sure about
Hulu. I haven't heard one way or another.