Horrors need a certain background count in order to come over, yes. But they need a much lower background count to STAY over, even though they won't be as powerful as they would when they could come over naturally. Think of it like a normal spirit in an area with a negative background count. The more powerful the spirit, the higher a negative count it can withstand. However, it would take something equally powerful to be able to draw them over in that state to begin with. Which is why the horrors were using the Great Ghost Dance sites to try and slip through. If a Named horror came over again, like the one chasing Aina did, then it would be able to stick around, at its reduced level. It would likely be mistaken for a shadow spirit, and would stay away from anyone who might recognize it for what it truly is, until it could bring over its friends. Some of the uber-powerful shadow spirits you hear about, such as the ones down by Bogota, could in fact be horrors that have slipped through before Montgomery shut the gate in Hawaii, and are only now getting to a level where they can actively influence events.