For a finite nonempty simplicial complex of dimension at most two, we prove that tightness over a field of characteristic two is equivalent to a complete one-skeleton together with symmetry of the link-component counts c_X(u,v) in every induced subcomplex. The proof adapts the cycle-link argument of Bagchi, Datta and Spreer and fills induced link cycles using mod-two fundamental chains of the resulting closed surfaces. Consequently, tightness over any field implies tightness over F_2 in dimension two. A four-vertex disk refutes the literal component-symmetry conjecture in the 2015 Oberwolfach report when neighbourliness is omitted; the theorem proves its neighbourly repair. This is an AI-assisted, self-audited, unrefereed preprint, not a claim of higher-dimensional field independence or certified absolute priority.
