Thanks for your response, but I'm still a little confused.
Here's what the Help says about the STOPPED_STATE_ENTERED event:
Dispatched when entering the stopped state. This happens when
you call the stop() method or click the stopButton control.....The
FLVPlayback instance also dispatches this event when the playhead
stops at the end of the FLV file because it has reached the end of
the timeline.
The problem I was having was that when a video finished
playing, another one had to load into the same player. I have a
listener listening for VideoEvent.COMPLETE, which runs a function
that calls the Play method to load the next video. But when the
first video finishes, AS acts as though the Stop button was
clicked.
The workaround I used was to capture the Out and Over states
of the player's Stop button. I then cropped them in Photoshop and
brought them back into Flash as a simple button, which executes the
Stop method when clicked. I then placed this button over the real
one. Since it has its own name and functionality separate from the
built-in controls, I can now separate the methods and events of the
button and player.
But I'm not crazy about the solution because I now have to
keep track of another object (esp. when moving or resizing the
player), and if I want to re-use the code elsewhere, I have to
create another button.