I don't think anyone is advocating dishonesty. Not reporting something when you are obligated to is a terrible idea. However, if the OP's charge was truly dismissed after completing probation, it says right on the application that he does not have to report it. This would not be a case of moral turpitude.
This is why it is of utmost importance for the OP to find out definitively if his charge was dismissed and he does not have a conviction. If he chooses to not report it without this definitive knowledge, then yes, that would be an egregious mistake.