Schools vary and the admissions staff has likely seen others from your son’s other school. They might know that a particular score or recommendation means one thing or another. Often when the kid has been the best in their class, the parents don’t really know where their kid is at in terms of other kids. My student had three kids in the math class last year all of whom were the best in their town. All had to drop down a level. My kid was not the best in the town and did extremely well. I think it depends on a number of factors not only background but also how quickly the kid learns.
I would let me kid go for a week or two and touch base in great detail ( even with the teacher if needed) to get a sense of the pace of the class and where your son actually is. Kids know if they are struggling compared to their peers. Or if it’s a cinch.
One thing you already know as a BS mom, many BS kids are talented in a particular area. So just make sure the talents line up. Being a new student and struggling could make for a tough year. And let your kid lead. I doubt he’ll want to be at the wrong level either. Sitting in a slow paced math class is boring.