I'm not sure how Virtual Keys work but perhaps that's conflicting?
No. You would have had to configure some Virtual Mapped Keys for this to be possible (which is unlikely to do on accident), and I would assume you didn't do that. All a Virtual Mapped Key does is replace one with another.
I dug around and found the repeater state action
http://isboxer.com/wiki/Repeater_State_Action so I thought I'd try to create a new map for my movement keys and bind an action to turn off mouse repeater first. I put the key map into "always on." No joy--all that happens is my toons stop following me and broadcasting stays on.
I'm not sure what you're showing is really what you want to do. Presumably you have Broadcasting Mode on, and you want to turn it off entirely instead of just the mouse part, and you probably want it synced with the broadcasting icon (assuming you didn't just remove it...). To do that, you can first use a Mapped Key Step Action to set "Activate Repeat" to Step 2, then a Do Mapped Key Action to perform "Activate Repeat" in Window:Current. This will disable Broadcasting Mode.
Secondly with this key binding you're broadcasting S to all windows instead of just the current window, so of course they will stop following you if you press this button (because they all want to move backwards any time you press S). Likewise, if you use a binding like this and set it to S goes only to the current window, then when you have Broadcasting Mode on and press S and expect it to go to all windows, it would only go to go to the current window... If you're going to use a mapping like this, I would suggest sending S only to the current window.
The screenshot doesn't show the Hold option, but you would also want Hold enabled on this Mapped Key so that you can hold it down to move.
You also probably don't want to bind "S" under "Always On", because at some point you're going to want S to do what it normally does instead of this particular behavior. You probably want to put it in the Non-combat Key Map (so it can be toggled off).
So in short... I would probably just do what Alge suggests. But if you're going to map your movement keys for this:
1. put them in Non-combat rather than "Always On"
2. make sure Hold is enabled
3. only send the keystroke to Window:Current
4. instead of using a Repeater State Action, turn Broadcasting Mode off via a Mapped Key Step Action to set Activate Repeat to Step 2, and then a Do Mapped Key Action to do Activate Repeat (doing step 2, which turns off Broadcasting Mode)