Keeping the air clean is a transaction, though (or rather a series of transactions). It requires exchanges of value (trade-offs). The positive and negative in externalities is not about some perceived social value; in that sense, economics, like any other serious scientific discipline, is value free. (Well, unless you're Paul Krugman.)
Using the word transaction was probably not the best; in economics, it has a meaning different from its common use.
From the Wikipedia article, you cited:
In economics, an externality (or transaction spillover) is a cost or benefit, not transmitted through prices[1], incurred by a party who did not agree to the action causing the cost or benefit.
The negative in negative externality is not a value judgment in the sense of moral or ethical values (for which economics, like any scientific discipline, has none), but an assessment of increased cost (including lost profit or lost potential profit) from an action to which you are not party. A positive externality is decreased cost or increased profit from an action to which you are not party.
Some examples:
1) I run a café and someone just saw the Virgin Mary in a piece of toast, and now my café is full every day for three weeks; my positive externality is my competitors' negative externality.
2) The pious Marians in the previous example crowd out my regular customers and once they're gone, some of my previous regulars don't return, a positive externality for my competitors.
While the same action does not always have positive and negative externalities, and they do not in any sense balance, the same action, decision, or market influence can act as both a negative and positive externality.
Because of the political process though, the factory operator does not have control over the decision to pollute certain substances; he was not given that decision: the very definition of an externality; it most definitely is an increased cost and therefore a negative externality for him. I'm not saying he should have that decision; I'm saying he doesn't have the decision. It is external to him.