>>Example:
>>The default UpdateSourceTrigger for a TextBox is LostFocus(). If I leave it that way and somewhere in code execute: TextBox.Text="Hello World" this is not relayed back to the source - until (and if) the TextBox subsequently loses focus.
>>To updated the source immediately I need to set the UpdateSourceTrigger to PropertyChanged. If I do that then the source is also updated on every keystroke.
>
>Wouldn't TextBox.Text="Hello World" remove the binding on TextBox.Text and replace it with the string "Hello World"? Since the binding on TextBox.Text is now gone, the source would never be updated.
>
>Or am I still not following?

Following completely - and I agree entirely that directly setting the Text property should replace the binding. The trouble is that is not what I'm seeing. It's been a long day and I may be missing something obvious but it you have time try this:
Code:

using System;
using System.ComponentModel;
using System.Diagnostics;
using System.Windows;
using System.Windows.Data;

namespace BindingTest
{
    public partial class MainWindow : Window, INotifyPropertyChanged
    {
        public MainWindow()
        {
            InitializeComponent();
            DataContext = this;
        }

        string theText;
        public string TheText
        {
            get { return theText; }
            set
            {
                if (theText != value)
                {
                    theText = value;
                    OnPropertyChanged("TheText");
                }
            }
        }

        public event PropertyChangedEventHandler PropertyChanged;

        void OnPropertyChanged(string s)
        {
            if (PropertyChanged != null)
                PropertyChanged(this, new PropertyChangedEventArgs(s));
        }

        private string s = "String A";
        private void SetTarget(object sender, RoutedEventArgs e)
        {
            TB.Text = s;
            s = s == "String A" ? "String B" : "String A";
        }
    }

    public class TBConverter : IValueConverter
    {
        public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
        {
            if (value == null) return Binding.DoNothing;
            return ((string)value).ToUpper();
        }

        public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
        {
            return ((String)value).ToLower();
        }
    }
}

XAML:

<Window x:Class="BindingTest.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525" 
        xmlns:local="clr-namespace:BindingTest">
    <Window.Resources>
        <local:TBConverter x:Key="TBC" />
    </Window.Resources>
    <StackPanel>
        <TextBox x:Name="TB" Height="31" HorizontalAlignment="Left" Margin="71,45,0,0"  VerticalAlignment="Top" Width="148"
                 Text="{Binding Path=TheText,Mode=TwoWay, Converter={StaticResource TBC}}"/>
        <TextBox x:Name="TB2" Height="31" HorizontalAlignment="Left" Margin="71,45,0,0"  VerticalAlignment="Top" Width="148"
                 Text="{Binding Path=TheText,Mode=TwoWay, Converter={StaticResource TBC}}"/>
        <Button Click="SetTarget">Set Target</Button>
    </StackPanel>
</Window>

The binding and converter still appear to be operating after 'TB.Text = s;' (you need to set focus to the TextBox and tab out to get the source updated or, better, just set the UpdateSourceTrigger to PropertyChanged)