Cocoa app to publish podcasts vs Mobile friendly site
It's not a podcast if they just upload files and tell you where to find them. The whole point of a podcast is that they are referenced explicitly in a feed of some manner, such that a utility can automatically make them available in whatever manner you need.

Like iTunes for example. It (by default) updates the feed occasionally, and downloads new episodes when they're available, suitable for immediate listening, or sync'ing and listening on-the-go.

Anything else is just silly, and probably means the site operator doesn't really know what they're doing.