They are not banned from using pedestrian paths, the speed limit is just set to the minimum amount to discourage pathfinding through them, though its obviously not a perfect solution.
It may be impractical to completely ban vehicles from pedestrian roads because the game has an overarching car-centric model, specifically with deliveries and emergency services.
Consider using Traffic Manager: President Edition to ban private vehicles from the road, or build dead end roads and connecting pedestrian paths to discourage vehicle through traffic.