It looks like mystery about lost update to myTextBlock.Text revolves around implementation specifics of event processing in Silverlight on WP7 (or may be Silverlight in general?).
Apparently, when assignment myTextBox.Text = ""; happens, "on text change event" is being added to the end of the queue of events waiting to be processed. So, queued event will be picked up for porcessing only after myButtonClick event handler completes. And when that happens, all your changes to the myTexBlock.Text will be effectively undone, lost or what have you. This is quite esy to validate by clicking "Clear" button without entering any text immediately after application loads, or clicking it twice in a row after some text was entered. In this case "on text change" event won't be fired (presumably changing text form "" to "" doesn't constitute a change). You'll note that text block won't display any text.
I guess a real take away from this episode is how easy it is to mess thing up big, whithout understanding what events are and how they are being processed at run time.