I've had this problem coming across sets and podcasts that only linked to iTunes subscription. (I hate how most media "has" to go through iTunes closed off service) Atlas, there is a solution for those who have weened themselves off of crApple's inferior iTunes and are learning there are better out there so as long as one has the will to learn!
SOLUTION:
Subscribe to the podcast on iTunes. Then in iTunes go to your Podcast section, right click the recently subscribed Podcast and copy the Podcast URL. Go into MusicBee and right click on Podcast to add a new subscription.
There you should go!