darius miles and stromile swift WANTED to leave their teams but couldn't do it because of the prospects of a matching offer. the suns aren't known as a cheap organization. current CBA rules mean you make and offer, and 15 days pass before you know what happens. this is a risk most teams will take only as a last resort.
on top of that, i would imagine the suns would themselves be negotiating with jj. on top of that, the new collective bargaining agreement will most likely lower his price. i believe max deals will be 5/6 years rather than 6/7, raises will be somewhat/dramatically less than the 12.5% they are now, and 'max' deals will be less than the 25% of cap that they are now.
add in the backlash that i believe will occur because of the uselessness of the excessive spending last summer (etan thomas, adonal foyle, derek fisher, etc), and i don't think there will be alot of bank breaking for jj.
furthermore, a successful season this year (2nd round or better) would make it a tremendous PR risk to let jj go even during the off-season. right now, the fans of phoenix are developing a relationship with the players, you don't want to mess with that. in the long run, making the payment may actually end up making money for the suns.