Impossible ChessKid.com puzzle?!?!

I was working with a student on ChessKid.com puzzles last week. Usually, I would find the solution within seconds while I waited for my student to find it. They were mostly testing basic ideas, such as mate in 2 moves or trapping the queen or along those lines. Then, we came upon the following puzzle (see board, black to move)... For once, I was puzzled. How can a ChessKid puzzle be this complicated?!?! I was calculating lines in my head and I still found that white was winning.

  Study this puzzle carefully before scrolling down and seeing my thoughts.... Good luck!

White is up a lot of material, and has mate threats coming against my very vulnerable king. Ra8+ followed by a queen advance seems to be winning for White unless Black finds something fast. Obviously, Qg1+ has to be the first move, forcing Kh3. Here, the only check is g4+, which forces Kh4. Now Black has Bf6+, but after Kh4, Black has nothing... What's going on???? Black has run out of checks. If gxf3 (which wins the rook), then white starts the checks with Ra8+ and Black is in trouble. Could this puzzle be WRONG?!?!?!

I eventually found out the answer to this puzzle, and it shocked me!! Study this puzzle carefully and comment  your ideas and lines. I will post the solution soon! Have fun!!