Thanks for getting back - So a few things:
1) Yeh, it makes sense when you think about it that the iPhone browser just "plays" - where would it put the file? So when you really think about it it makes sense I think.
2) The weirdness of this whole thing is this - when I have the Download Shortcode wrapped around the mp3 - the file will 'stop playing' in the middle but only when on headphones. Weird right? I did some research - here is my suspicion --- when the Download Shortcode is used, it is initiating some background process that eventually fails on the iPhone - when the 'fail' happens it disrupts the headphone feed. Sounds so weird and random - but you can read about people complaining about non-iTunes mp3 files playing strangely on headphones.
My solution has been to include 2 links - one that has the download shortcode and one that doesn't - the 'plain' link I have marked as "play now" - and when you use that link there is no disruption in playing when on headphones.
Oddly - both options will play fine when NOT on headphones -- but the 'download shortcode wrapped' version will not show the length of the file.
You can see this behavior yourself - the page is: http://partnersinmindfulliving.com/fun-stuff-extras/audio-recordings/
Anyways - this is such a random little thing and this is probably too much information - but I spent some time yesterday so thought I would just pass that along.
I do still Love the Download Shortcode plugin - it works like a champ and I will for sure use it again. Thanks!