So if a shaman spent all his Magic Points to summon a big elemental (say: a salamander), the Sorcerer can't use his Dominate (Salamander) spell to tackle it ? Or - when the shaman's companions actually kill the spirit, the Initiate won't be able to bind it with his enchanting skills ?
The three styles of magic are not forbidden from interacting: Sorcery has the spell Spirit Block for example. If the sorcerer learnt Dominate Spirit, he could do exactly that. But it wouldn't help against a priests' companion for example.
Elementals are a bit different. All the styles of magic interact with the Runes, including the Elemental Runes, so a sorcerous Dominate (Salamander) would work fine.