In the podcast a link is offered to open the feed in iTunes. This allows subscription on an iDevice, but only after synchronizing via the desktop iTunes application.
The problem is that for the desktop iTunes the protocol handler to be used is "itpc" while on iOS it is "feed". Thanks Apple, very logical...
Since nowadays many users do not sync with desktop iTunes anymore an explicit iOS button is required.
If anyone knows how this works on android, please let me know.