No. Portland can be proactive, since they own bird rights and can sign him for a year more for more money. Similarly, in the Suns sign/trade scenario, that extra year and total of money matters. Yes, Spurs can outright sign him to a 4-year MAX. Via Sign/Trade Suns could offer 5-year Max, and offer Portland a bundle for Aldridge. Spurs aren't offering 5-year Max, nor helping Portland recover with multiple 1sts and quality-priced young players.
So, yes, Spurs are in drivers seat, but both Portland and Phoenix can offer more money, more years.