The SO team doesn't seem to like the idea of an RSS feed for recent responses. This feature request has been around for months and they made the Recent page private so our old Yahoo Pipes solution won't work anymore. If someone developed a way to authenticate and get this page automatically, and then generate a feed, would the SO team do something to prevent this?
No, they would not, unless you were pulling too much bandwidth from their site.
All of the things that you state don't make a case for why they wouldn't allow you to programatically access that page.
The recent page (envelope) is private because they don't wan other users to be able to see what other users have been doing to you on the site. And the feature request has been around for months just like 90% of all of the other feature requests.