I got a reply from someone at Mule (whose name I didn't recognize) that said that they did not like Stitcher's business model. This strikes me as strange because I figured that the larger the audience, the better deal the podcast is giving its sponsors. But, no, apparently they don't want Stitcher to host their podcast and then serve iAds (which I ignore) in the app. But yet they have no problem with Apple hosting the podcast on their servers.
This really sucks because Stitcher does a lot of things that lend to a great user experience including (but not limited to) transcoding the podcasts so that they can be efficiently streamed.
Hopefully this new app from Apple will allow me to gather my podcasts under one umbrella.
Edit: Ugh...no, this new app is nowhere near as pleasant a user experience as Stitcher.