Is it manipulative to optimize the tag line on your landing page? You're trying to persuade a visitor to buy your product. Or are you trying to manipulate them to buy your product? The same principal applies to keeping customers.
I'd call this manipulative when it becomes disingenuous. For example, had they put actual speech bubbles above my friends' heads and led me to believe that they actually were asking me to stay. Until then, this is roughly akin to saying "Hey man, don't leave the party yet. We haven't had cake yet!" To which I'd reply "OK, well twist my arm why don't you" and then eat some cake.