Windows Phone: NullReferenceException in HttpWebRequest.Headers.set_Item

Not much else to say--I hit this on WinPhone, but not other platforms. This code gives me a NullReferenceException if it's part of the Unity project (i.e. in Assembly-CSharp.dll):

 HttpWebRequest r = (HttpWebRequest)WebRequest.Create("http://www.yahoo.com");
 var h = r.Headers;
 
 h["header"] = "appId";

But the exact same code in MainPage.xaml.cs works fine. The only thing I can guess is that code from the project itself is somehow using System.Collections.Specialized.NameValueCollection from WinRTLegacy and that version has a bug for setting values. Otherwise I'm at a complete loss.

Any ideas would be most welcome.