The High School rule book 7-6-1 says: "... The thrower shall release the ball on a pass directly into the court ... . The throw-in pass shall touch another player (inbounds or out of bounds) on the court before going out of bounds untouched."

So, if A1 is the thrower and B1 (who is standing with one foot on the sideline) catches the throw, which player violated? Did A1 actually "pass directly into the court" when he threw it to an out-of-bounds player?

A related question is this: Was the ball ever legally "in-bounds"? If not, how can B1 cause - a ball that was never in bounds - to become out-of-bounds?

Did the ball leave A1's hnads? If yes, it is a legal inbounds pass. In this Case B1 has violated. Your chicken and the egg theory should go something like this...
B1 caught the ball making it a legal inbound pass. He was touching the line, which makes it a violation. The fact he is touching the line does not negate the fact the ball was inbounding.