On the $p$-adic distribution of torsion values for a section of an abelian scheme

Let A -> S be an abelian scheme over a p-adic field, and let s : S -> A be a section. We study the torsion locus boolean OR(n >= 1) s(-1) (A[n]) on S, and we show that torsion points on S of different orders stay away from each other.