It's sorta misleading. The guaranteed portions of all contracts signed under the new CBA are automatically stretched upon the player being waived. Using the provision only allows the team to count the stretch over three cap-years. In Nash's case, if the Lakers were to buy him out for $6 Million, they could choose to either take that all on their cap next session or use the provision on it and only take $2 Million each of the following three. If they just waive him without a buyout, they can choose to take all $9+ Million next year or to use the provision on it and take $3+ Million each of the next three years. Regardless, they would actually be paying him over three years.
The CBA FAQ is linked in the OP of the Trade Thread. It explains the stretch provision clearly.