I don't disagree that this is dishonest behavior, as a son I'd prefer the bullying to discovering this. That said, your cavalier attitude about how she should just "find a real father" is not appropriate either. If she was battered, as the answer implies, it's completely expectable that she has trust issues with starting any new relationship, let alone bringing someone into her daughter's life.
Japan may be full of single men, and I'm sure many are wonderful people, but she already failed once in her judgment, so how can she trust herself not do to it again? Is it laziness to avoid swimming after you've almost drowned before?
Plus, you're actually reinforcing her position, by treating "a father" as something you just go out and get, like a car. What if she simply doesn't want to be intimate with anyone? How many single men are prepared to be a father without being a husband?
What you're essentially saying is that you agree that she should hire a father for her daughter, only that she should pay with her body instead of her money.