C# - HttpWebRequests Sends Parameterless URI In Authorization Header

I'm connecting to a web service from .NET, like:

var request = (HttpWebRequest) WebRequest.Create(uri);
request.Credentials = new NetworkCredential("usr", "pwd", "domain");
var response = (HttpWebResponse) request.GetResponse();

The authorization header looks like:

Authorization: Digest username="usr",realm="domain",nonce="...",
uri="/dir",algorithm="MD5",etc...
^^^^^^^^^^

The server returns (400) Bad Request. A header send by Chrome or IE looks like:

Authorization: Digest username="usr", realm="domain", nonce="...",
uri="/dir/query?id=1", algorithm=MD5, etc...
^^^^^^^^^^^^^^^^^^^^^

We suspect that the difference in URI is causing the web service to deny the request with a 400 error. Is it possible to make HttpRequest send out an Authorization header that includes the full URI?