I have only ever used fire ant specific pesticides. They're just a problem in my area.

If you’re having a problem with fire ants it’s likely due to overuse of broad spectrum pesticides. Fire ants have tons of natural predators, but they are usually taken out by broad spectrum pesticides a lot more effectively than the ants.

Let me preface this by saying, I agree with your overall message about avoiding broad spectrum pesticides in the lawn, but I'm curious where you got this information from your first paragraph?

I ask because these things seem completely at odds with my experience and with most of the information I've read about fire ants.

I really don't know anybody that uses broad spectrum pesticides in large areas of their lawns or gardens, but fire ants take over yards anyway. I certainly don't use them here and none of my neighbors do.

While fire ants may have tons of natural predators in their native territories, the issue in most of the areas where they are invasive is that there aren't any/many natural predators that are actually capable of keeping the populations under control. They breed and migrate so aggressively that critters who predate them don't make a dent. And the native ants don't have much defense against fire ants.

Additionally, I'm not sure there are any current nematode products available in the US that are known to be effective against fire ants. Doesn't mean that won't change or that there aren't new products I'm not aware of, though. Just saying, that general consensus is that it's not a viable solution.