Responses
I reread this too. But then in that angle it was not really obviously shown if it was on the hips or just looks like it or he was just holding the door. It was all a story gossiped by the nurse to Akira. Akira didn't see it personally. He just made the image based on what the nurse told him. This is my take

I'm rereading this and chapter 2 doesn't sit well with me. Not a single decent person would have his hand around his potential kid's babysitters back like that. That is weird. There is a reason that that position has always been used for romantic partners in real life and in fiction. If you want to meet a potential babysitter use your words and don't touch her like that. It's not like the misunderstanding was caused by her being his car or him opening the door for her to enter the building, both of which are acceptable. His touched her lower back.