I frequently use software specifications as a counter argument to this. Non developers can't write specifications without leaving out major key bits in the information, my point then would be that since they are not constrained by limitations of programming language but only their own expressions in written text that should not be a limiting factor.

Your example is extremely simple and could work for a new coder but once things get just slightly more complicated things get messy. I can already find exceptions in your very simple example: how exactly are user supposed to be alerted? Do all users have a mobile number so they can be texted? If not do you try email? What if they are online, do you send an im-message? Should you send to all available addresses? In which order do you prioritize message if you only send to the first available destination, email first or sms first?