It’s nonsense, based on the slimmest grain of truth, you would need to show ID for credit checks if buying on contract or finance. That's the only reason.
But you could easily buy a second hand phone from a high Street resale shop and they won't ask you for ID. You don't need ID to buy on Amazon, buy vouchers in a supermarket for Cash and you can buy a phone without using a credit or debit card.
They don't ask for ID, they might ask for a one time password based on value. I had a Stanley knife delivered the other day and driver asked for date of birth not ID.