Omg guys. I think I might have found some circumstantial evidence.
So I started skimming the script for contradictions to this theory, and instead I found this... (I kinda got excited and decided to post about it right away, so I'll let you know if I find anything else later.)
Phoenix: Larry Butz... my best friend since grade school.
Our school had a saying: "When something smells, it's usually the Butz."
In the 23 years I've known him, it's usually been true.
So, what we have here is Phoenix telling us that he became friends with Larry in grade school (presumably after the lunch money incident), but he's known the guy for 23 years. This is in Case 1-1, when Phoenix is only 24 (and I guess Larry is only 23!). This means Phoenix knew the guy since he was around 1 year old. Either their parents were friendly (which I doubt, or else they probably would have become friends earlier), or this is some decent evidence pointing to the orphanage theory.
Banking off that, if this did turn out to be true, I would hazard a guess that Larry probably wasn't in it for the long run, like Phoenix. I don't think a place like that would let you drop out of high school without a fuss, honestly (and we know Larry didn't graduate high school).
Of course, this raises the question of what was the deal with Larry's parents...but I guess that question was already hanging for a while. It probably wasn't terribly "functional" though. Maybe he went in and out of their care. /random theorizing
I have definitely gotten the sibling vibe from the two of them though...even if they don't think of themselves that way. And Larry's kind of a jerk to Phoenix at times, but that's what siblings do, right? :3