Not sure you read the article - there is an additional constraint in that only email addresses pertaining to the institution in question are allowed.
The article suggests performing "server-side membership testing, which is O(1)", but I think this is a bit too much — you can do even easier server-side validation without the list of all valid e-mail addresses, just the information that "@[anything but these two domains] is not an OK target".
Then the customer won't pay you because you ignored their requirements. They might even sue you because you breached contract.
If the customer asks you for a mound of poo you write them a mountain of poo; you try your damned hardest to make sure that the room smells like poo when they are using the app. If they go home and tell their wife and kids about the giant mound of steaming poo they have been using all day then you have succeeded because they will go back to the one developer who knows how to stick to their senseless requirements.
At the end of the day all the other developers are giving them apps built on principles that only make sense to developers - principles that only really make sense for millions of users and not the few thousand that they have. Principles don't put a house over your head and food on the table - money does.
It does if you want to give the user instant feedback when they type an address that is in a valid domain but does not actually exist, as Ntrails pointed out. If you think a requirement doesn't make sense, you're supposed to ask the client, not just arbitrarily ignore it.