You are right.

However most proofs of the hairy ball theorem also prove the converse, so that there is a continous non vanishing tangent vector field on uneven dimensional sphere surfaces.

This can be extended to all 3 dimensional surfaces in 4 dimensions homomorphic to the sphere. The ant walking can follow the vector field and solve this problem topologically.

My point being that the HR goon following the expected leet code solution might not understand this because they might expect the "approved" graph theory solution rather than an alternative approach.