They can take the role of a VC for a startup - providing capital. EA can absorb a $10 million budget for a new game, where Rovio might have difficulty convincing a bank to loan them that much.
They probably didn't get an advance as Rovio still own the product and the brand. You also would lose more than the 10% revenue share figure quoted elsewhere in this thread if you got an advance. Though I also doubt Angry Birds cost $10 million to develop.
I'm not saying Antry Birds cost $10 million, I'm making a general statement on why iPhone developers might still want a publisher. Rovio didn't sell to EA at all.