Will a using clause close this stream?

Yes, StreamReader.Dispose closes the underlying stream (for all public ways of creating one). However, there’s a nicer alternative:

using (TextReader reader = File.OpenText("file.txt"))
{
}

This has the added benefit that it opens the underlying stream with a hint to Windows that you’ll be accessing it sequentially.

Here’s a test app which shows the first version working for me. I’m not trying to say that’s proof of anything in particular – but I’d love to know how well it works for you.

using System;
using System.IO;

class Program
{
    public static void Main(string[] args)
    {
        for (int i=0; i < 1000; i++)
        {
            using(StreamReader sr = new StreamReader
                  (File.Open("somefile.txt", FileMode.Open)))
            {
                Console.WriteLine(sr.ReadLine());
            }
            File.Move("somefile.txt", "somefile.bak");
            File.Move("somefile.bak", "somefile.txt");
        }
    }
}

If that works, it suggests that it’s something to do with what you do while reading…

And now here’s a shortened version of your edited question code – which again works fine for me, even on a network share. Note that I’ve changed FileMode.Create to FileMode.CreateNew – as otherwise there could still have been an app with a handle on the old file, potentially. Does this work for you?

using System;
using System.IO;

public class Test
{    
    static void Main()
    {
        StreamWriter creditsFile = new StreamWriter(File.Open("test.txt", 
                                          FileMode.CreateNew));

        creditsFile.WriteLine("code\\inc");

        creditsFile.Close();
        creditsFile.Dispose();

        File.Move("test.txt", "test2.txt");
    }
}