[Adverblessly]

Indeed this is not a second factor.

I assume this restriction is against automation. As a complete guess on the heuristics: If the phone number you gave them is a "virtual" one, you are out. If it was used too frequently for recovery, you are out. If they are already familiar with it as belonging to someone else who is unlikely to also own the current account, you are out.

With those heuristics you need to provide a "fresh" phone number that likely belongs to a real person and costs real money to purchase and you are unlikely to want to "burn" for just 5 out of 5,000,000 of your automated attempts.