I doubt he told them he left her on the side of the road. He could’ve made up any story that would be believable.
Gabby and Brian were on a cross country trip LIVING in that van, it was her home. It was going to be the source of her income from her travel vlog (or whatever it was). They were engaged and she lived with them, presumably they would know these things. Their son returned in the van they were living in, she wasn't with him. They are really going to just assume Gabby decided to give up her home and her dream and stay across the country? Let's say they did assume that based on what he told them, the minute her parents contacted them looking for Gabby they knew something wasn't right about his story, otherwise they wouldn't have hired a lawyer and ignored their future daughter in law's parents who were desperate to find her. They knew he did something to her, they may not have wanted to admit it but there is no way they didn't know.