Re: Fruit of the poisoned tree
"But evidence is evidence. If I trespassed on your property and saw you stabbing someone, does it mean that it didn't happen because I shouldn't have been there?"
That's not considered Fruit of the Poisoned Tree. It covers police procedure in that they have to play things by the book. That means they can't seize evidence without proper authorization (such as a search warrant or acting in the immediate context of an arrest), interviews can only be conducted after the speaker is fully aware of his/her rights (the Miranda decision et al), and so on.
To understand it a little better, consider the Adam-12 episode "Courtroom" (Season 2, episode 9; Adam-12 is well-recognized for its attention to realism). A man was arrested in his house for outstanding traffic warrants, but during the follow-up, an illegal pill mill was discovered and confiscated. Since the confiscation was not germane to the original arrest (and a search warrant was not obtained to confiscate it properly), the evidence was declared inadmissible due to Fruit of the Poisoned Tree, and the case of illegal drug manufacturing was subsequently dismissed.