I have had successes with children who have been learning using the Suzuki method for up to four years before they came to me. They could not read a note, which was actually not the most frustrating part - the worst thing was, because they are taught to find the sounds by listening, they will play wrong note after wrong note until they work out the right one, and then they continue with the rest of the piece. This is completely opposite to the way I was taught, which is you know the right note and you hit it, and you certainly don't hang around on a wrong note until you get it right - you keep going, and make sure you correct it during practice time.
I don't know about the Suzuki method, so I don't know if this just happens to be these kids - one child in particular had this bad habit ingrained very deeply, so maybe her teacher just applied the methods incorrectly.
But the way I taught these children to sight-read is simply to concentrate more on sight-reading. I kept them on pieces around the same level that they were at when they came to me, I don't see the need to bore a child with a beginners piano method when they have already been playing for some years. But I actually have a separate part of the lesson devoted to honing sight-reading skills, and I simply gave Suzuki-background students more of that sort of time, and taught that part of the lesson more intensely. It takes some time, but they do catch up.