Fruit of the poisonous tree assumes that the real way they identified the target was through illegal means. It doesn't have to. Could be an anonymous tip, a suspicion from the police, etc.
But bear in mind that typically we read "illegal means" as some sort of deliberate violation of the law, whereas in the US it's more like there's a relatively carefully defined set of "legal means". There are a number of sources of inadmissible evidence that a common, normal person would probably consider perfectly moral to introduce as trial evidence, but is denied in the US. (At least, officially. Of course things can be cheated. I'm talking about the nominal system here, not the real one.) "Illegal means" means less in this context than it might normally.