It's a hybrid app, views written in HTML5 & CSS3, and wrapped on the device. Navigation is native.
(Source: the post)
I assume he is referring to Basecamp Classic Mobile [1]. Reading the post, it seems they thought HTML5 was the "way to go" because they had more experience with the technology, not for any particular technological reasons.
Chances are that in a year or so, they'll release a completely native app. That seems to be the trend now - go HTML5 initially to get an app out fast, then create a native app later.
All of the content screens in the app are still HTML5. Because of that direction, we now have a native experience on iOS AND a solid mobile experience in the browser. HTML5 still offers the greatest reach, a superior layout model and the fastest development. It's a myth that web views are inherently a poor experience.