Where that stops being true
Two different approvals sit behind that sentence, and a repair can trip either one.
Zoning decides the height: 6 feet in side and rear yards, 3 feet in the front 20 feet, and 3 feet inside the corner triangle. Going to 7 feet needs a planning permit and the adjacent neighbors' written consent — and height is measured to the top of the posts and any lattice, not to the top of the boards, which is how a topper turns a compliant fence into a non-compliant one.
A building permit is the separate question. Coming back in vinyl, metal or masonry instead of wood needs one at any height; a retaining wall always needs one; and a wood fence above 6 feet needs one on top of the planning permit. Keeping the repair like-for-like is what keeps both answers "no" — the fence rules and permits guide sets out where the line falls in each of the three cities.
Next step
Photograph the base of the leaning section's posts and the full run — send through the form for a count and range before anyone drives out.