Ambulance EMTs are trained to be really forceful about it if they think you need to go in. Years ago I was at a neighborhood ice rink skating with my kids when a lady out skating with her own kid got hit in the head by a hockey puck hit with a slap shot that had escaped the hockey barriers. It knocked her out cold, though only briefly, so from her perspective, she was skating along minding her own business and then she was lying on the ground in intense pain with no idea of where her child was. I skated over and reassured her that her kid was RIGHT there, sitting next to her on the ice, completely unhurt, and then I took her phone and dialed 911 for her. Fire arrived first and was pretty casual about hoisting her up into a sitting position. She was still in pain but talking about calling her boyfriend and having him drive her to an urgent care to get checked out. Then the ambulance pulled up with EMTs who side-eyed Fire and put her in a cervical collar and wheeled out the stretcher and they were (correctly!) very firm that she needed an ER. (First of all, she had lost consciousness -- she said no, when they asked, and I corrected her. People hear "loss of consciousness" and picture the movies where you're out for hours. She was out long enough to hit the ice and not remember falling, that's loss of consciousness. She absolutely had a head injury and that needed to be evaluated. Second, I didn't think of this until they put the collar on her but YES, this injury could have fractured cervical vertebrae, and that absolutely needed evaluation.)

They didn't even talk her into it per se, they just acted like it was very obvious that a hospital trip was what comes next for something like this, and she went along with it. Her boyfriend came to the park and took charge of the little kid.