Can an Outsider with the Native subtype be summoned with a spell? If so, under what conditions, and what spell? If not, why? Other than needing to be summoned to a plain different to the one it's native to, I can see no reason why it would not meet the conditions of a Summon Monster spell.
So according to Summon Monster:
Which brings the question: can a Native Outsider be Extraplanar?
So yes, while not on the Material Plane, a Native Outsider would have the Extraplanar subtype (Native and Extraplanar are not incompatible), and therefore be a valid target for summoning.
However, Summon Monster has already clearly defined Summon Lists which don't include any Native Outsider, meaning they would have to be adapted. There is also the problem of level: when summoning a monster, you just get the basic one, not a version with classes. So it could be argued that Summoning an Aasimar (for example) would get you the Lvl 0 version. I would see several ways of doing it, but that would definitely be in the houserules domain.
So, while an Outsider (Native) is theoretically a valid target of Summoning in RAW, the actual mechanisms of it would have to be houseruled by the GM.
So except for the fact that Summon Monster has a set list, you could argue that you should be able to summon "native outsiders" (that is, from the Prime Material) if casting Summon Monster from a non-Material plane, as they are technically extraplanar.
However, you have the humanocentric nature of the game to deal with philosophically. Planar Binding works on outsiders and elementals - not Prime folks even if cast in Abbadon. You appear to be coming at it from a Planescape-esque "all planes are created equal, just different" viewpoint while the Pathfinder cosmology tends more towards "hey, these are special spiritual planes where gods live" - they are quite literally the spirit world, not "another Prime Material that just happens to be hot and have a lot of sulfur around."
Having said that, you can craft your game world how you like, and if you like the more "cosmopolitan planes" conceit you can certainly extend all the spells to work that way.