In case you don't know, there is a website called join.me which lets you do screen sharing from a browser, using a flash program that is on the web page.
Until I encountered this service, I had no idea that flash was able to do screen reading, as opposed to simpler tasks like using the web cam. But if it can do that, could it not also be recording keystrokes, storing all data from a session for someone's perusal, or the like?
Once you trust a website to provide a viewport into your company's computers' screens, who is to say that they will not be sharing details of the session? And given the nature of flash, who's to say that the session is really closed just because you close the browser window?