I would say that your friend is somewhat mistaken. Old motor mounts are squishy and less supportive; that is true. But as far as vibrations, I don't think that old mounts would contribute to that at all. If anything, they may lessen idle vibrations, or other vibrations, because of the fact that they ARE softer. But as for when to replace them, it really is a case-by-case scenario.
If you are getting "shift-shock", or excessive movement of the motor/transmission assembly when you or the car shift(s) gears, it may be time. Also, engage your parking brake, pop open the hood, and watch your motor (or have a friend look) and see how much it moves when you start the motor, switch gears, etc. My friend had an old Cavalier that had VERY bad mounts. The motor would move back and forth about 3", just from changes in idle pattern! (like on a cold start, as the rpm's drop and the computer slows down the idle and adjusts the air/fuel mixture). I ended up just putting in some polyurethane motor mount inserts in the motor mounts; it firmed them right up! Made them a little firmer than stock mounts when new. This is a much cheaper alternative, and it is likely that something like this is available for your car. The only downside is that you may get a little vibration when the a/c is on (because of the firmer mounts), but the whole driveline is more secure, and you can feel it, especially if you drive a stick.