Well I figured out a work around. I'm making the call from a keyboard hook used to implement a hotkey. The call works as expected if I put it into a BackgroundWorker with a pause. It's a kludge, but I have no idea why it wasn't working originally.
void hotkey_execute()
{
IntPtr handle = new WindowInteropHelper(Application.Current.MainWindow).Handle;
BackgroundWorker bg = new BackgroundWorker();
bg.DoWork += new DoWorkEventHandler(delegate
{
Thread.Sleep(10);
SwitchToThisWindow(handle, true);
});
bg.RunWorkerAsync();
}