Why would a team have to be under the cap to accept Googs in a trade?
Because the rule is, if a team is over the cap, any salaries they accept in trade must be within 15% of the salaries going out. (You are right, it's 15%, not 10% as I said before.) There is a $100,000 fudge factor allowed, but that's basically irrelevant when dealing with salaries this large.
If a team is under the cap, then they can add salary in a trade without having to give up the same amount of salary in return. So, for instance, the Nuggets could trade Nene Hilario for Gugliotta, once their current year's contracts expire. It is unlikely that Denver would go for this trade.
The trade Kicker has no effect on the trade dollars.
I don't think we know the specifics of Gugliotta's trade kicker, but in general this is false. Trade kickers usually result in a higher salary for the player after he is traded, during the entire remainder of the contract.
Outlaw's salary went up when he was traded from the Magic to the Suns. If I remember correctly, his salary with the Magic (had he stayed with them) was to have been $5,500,000 in 2003-04 and $5,000,000 in 2004-05. Now with Phoenix, those figures are $5,955,000 and $5,355,000.
That means that the suns could have an outgoing trade value of 11.7 million (googs contract) but are only required to take back 9.9 million. That would save almost 4 million dollars.
If not for the trade kicker, that would be correct. No matter what the trade kicker is or how it is figured, however, its presence means that the Suns would have to take back more than $9.9 million in salary. This is because the other team would have to give up more than $9.9 million, in order to be within 15% of whatever Gugliotta's new salary is (either a flat extra fee, or a percentage increase).
Still, you are correct that trading Gugliotta could potentially save the Suns a couple million dollars this year, if they happened to find the perfect deal with a willing partner.