I'm thinking of using APPMobi to push to the IPhone. APPMobi allows you to code in html and javascript and tap into your phone's functions.
This opens up the obvious desire to code an ASP.NET MVC app that calls these javascript methods.
I wondering if this behavior would violate Apple's TOS because they wouldn't have control of how we update our site.
No it does not. Ignore the person about about "downloading code at runtime" - it doesn't pertain to html/javascript/css.
The issue is if your page does a redirect to your site only. You're best bet is to design the UI in html/javascript and let that live in the app bundle, then use web services to make calls to get data.
Apple will deny your app if it's just you're mobile website embedded.