The fact is that you can not like flash (TW) or any other object inserted into web page.
If you want facebook like button in Virtual tour (means - in flash) - it is possible to do that, but all the approaches are just workarounds pretending flash being websites (or something like that).
If you want to see what it takes to make flash LIKE button, read here: http://labs.byhook.com/2010/08/03/facebook-like-button-in-flash/
In short - html overlay is a good and proved way to make LIKE button.
If that would be as easy - there would be tons of flash applications with facebook like icon.
Overlays are much much much easier and it is a natural way to add LIKE button. Facebook Like button workaraunds would work until facebook would change communication protocol. If facebook would change something - all your tours which rely on flash workarounds would break, but overlays would survive, because the html(overlay) button is being created by facebook itself.
Imho, it is in your interests to use overlays ;-)