You cannot start a new account with owned equipment that you've obtained elsewhere, that is true. But as I specifically stated, DirecTV has offers designed for those who can't provide SSN information or otherwise need to own their equipment, and that equipment is sold, on a one-time basis, at a significant discount. Only NEW customers qualify for this deal.
You're combining two different things actually.
There is an option to get an owned new customer deal. It's pricey and has set equipment options. You cannot mix n match equipment like you can in the leased deal. It ranges from $150 - $250 plus an activation fee. There are also limitations on getting other equipment on the account for a set time frame. The option is really for people who would want service for a short time frame to try it out.
The deal for people without SSN is still leased they just have to pay a fee to get service which gets refunded over the life of the account. Those people still have to pay for advanced equipment and a higher fee.