Ohtani isn't an idiot. He's someone who trusted his interpreter, a guy he's known for 20 years.
I listened to Tim Kurkjian give an interview a couple weeks ago. These interpreters have only slightly less than power of attorney over their athletes when these guys come to the US. Tim mentioned how yes, they would even do things like set up bank accounts for players.
It's incredibly easy to see how this could be pulled off without a player ever realizing it.