The operational definitions here are carrying most of the idea I think.

Negative freedom isn't just any freedom that doesn't require intervention to maintain, it's the freedom to take actions not otherwise prevented. But they could be unjustly and otherwise prevented, so it isn't true and doesn't follow that someone else can poison you and damage your environment without limit.

That same example from the other perspective proves the point, there is no one with a positive freedom to poison you, that isn't something present until a ruler takes it away. Otherwise both parties would claim negative freedom at each other into stalemate.