Very painful yes, but their "deadliness" is often overstated. As a normal, healthy adult you pretty much have to be allergic to die from their sting. Anyone who's allergic can go into anaphylactic shock, but the treatment, which is very effective and easy to administer, involves standard anti-allergic measures (e.g. adrenaline, not any specific antivenom) available in hospitals around world. Anyone with known allergic reactions would usually have an epipen. The allergic rate has been estimated at <3%, which is only about twice the number for ordinary honey bees. There are people that die from honey bee stings every year, but there aren't many people that talk about their deadliness.
Not saying that I would want to get stung by a bulldog ant as it definitely is very painful; just that the actual risk of dying from it is quite minimal.
