Didn't they basically pimp their son off to her with an approval letter already though? That doesn't count?
This was all the parents left behind for her. That is absolutely not a get out of jail free card for her to have sex with him. It might not even count as a pass for her to be taking care of him in their place, to be honest. You wanna bone an underage person in Japan with zero risk of legal ramifications? Marry them. But, the ages on that possibility are different for male and female as well. If he was a girl, 16 would be fine but he's not so it's gotta be 18.
Since I don't think he's there yet and there's no reason to assume his parents will accommodate them with signatures on legal forms when he turns 18, they can't get married until he's 20. Him being 18 may or may not be good enough on its own anyway, I forget what the deal there was. Basically, the laws over there are more open to people boning underage girls legally if the parents are cool with it either way though. Probably because they want the male to be old enough to take responsibility if he fires a critical hit with his baby batter. I dunno.
TL;DR: He has to be at least 18, might even need to be 20, for them to have a sexual relationship without neighbor girl getting Onee-san arrested.