First of all, as you have already conceded, ANY AP Calc (be it AB or BC) for a 10th grader is VERY advanced.
Second of all, as even the most advanced students –– the ones with 4.0 unweighted GPAs that have taken the most advanced courses available to them –– still get rejected from schools like Stanford all the time. By the same token, students without 4.0 unweighted GPAs also get accepted to schools like Stanford.
If we were discussing your son having to choose between either of the AP Calc classes (AB or BC) or regular a Calculus class (not AP), I would say yes, taking a lower-level (non-AP) might be not look great for a school like Stanford. Likewise, if your son were a senior and wanted to go into CS or Engineering, I might encourage him to take BC over AB.
If the normal progression in his school is AB followed by BC and he’s a 10th grader, he’ll still be able to take a more advanced class (e.g., Multivariable Calc or Linear Algebra) his senior year.
At some schools, however, the normal progression is to take AP Calc AB or BC –– not both in succession. At my D’s school, most kids don’t take Calculus until 12th grade.
The bottom like is this: your son’s getting into Stanford will not be determined by whether he takes AB or BC this year. He should take whatever class would be best for him overall without causing undue stress, lack of sleep, or sacrificing time that that can otherwise be spent on extracurriculars or time that he can be with friends and family.