What happened with Lebron and Cleveland and also Bosh and Toronto is not applicable here because both those guys didn't need sign and trades to get to their new teams. As a result, Cleveland and Toronto weren't in the position to ask for more than the low first round picks that they got. With Nash, the only way he can sign with the Lakers is for Phoenix to participate in a sign and trade. For helping out a conference foe along with a franchise icon, I think they would ask for more.
The differences are pure semantics. It is very much applicable. Sign and trades happen all the time and for a variety of reasons. Why did the Clippers sign and trade Reggie Evans to the Nets? Reason: something is better than nothing. If Nash signs with Toronto as a free agent, Phoenix gets nothing at all.
A low first round pick is better than nothing at all. And they would get a large trade exception back, which as we have seen can be very valuable.
It wouldn't behoove a rebuilding Suns team to not try to get something here due to a former rivalry. The Suns and Lakers are non-factors to each other in 2012. The Suns can't afford to punt away assets, no matter who they come from.
If they asked for more and the Lakers couldn't offer more, he'd sign elsewhere and they'd get nothing. Nash is a free agent. He has the leverage here, not the Raptors, Lakers, Knicks, Mavericks, and especially not the Suns.
Plus, you would think helping a franchise icon would be important to them, should he choose the Lakers.