dougp:
Solenoid driven ball valve?
That picture is quite strange:
Maybe they mixed up their product photos?
Are you suggesting using the ball valve to pinch the tubing off, that's an interesting idea! Or are you merely suggesting that it should be used for its intended purpose? In that case I would consider a standard solenoid valve instead, which should be cheaper than a ball valve. They do require constant power to stay open but that most likely isn't a problem for this application and can actually be beneficial to give a default cutoff in the event of loss of power.
Usually when people are using the pinch valve it's because they can't expose the fluid to the materials of a valve. This could be to avoid contamination or to make it easier to completely clean the system.