Not the person you asked but I’d guess it has to do with managing the emotions or anxiety that lead to the bad behavior. The way I think of it is I don’t want to teach the dog to overcome negative emotions, I want to help them not have negative emotions in the first place. If possible.

This, exactly. I think that the idea is to teach to dog how to interrupt the negative emotion with something positive. It gets to the point where they interrupt it themselves without your intervention. With Lily, it got to the point where she'd see a small dog or a cat, and she'd look straight up at me (good girl!)

To begin with, practice randomly when there is no trigger. Have a sneaky treat ready and say the dog's name. If it's difficult to begin with (because they don't know their name), try putting the treats into a small plastic container and shaking it, or taking the plastic packaging of their treats. They learn to respond to that noise very quickly. Words are more complex, but if you say their name when you make the noise they'll start responding to that too. Always carry accessible treats.

5 months since we adopted untrained (pretty wild) greyhounds, I can get either of them to sprint to me by calling their name, sit, high-five, lie down... no matter what's going on around them. That response makes it easier to discourage cat-chasing and to reduce their prey drive.

I think you're approaching it from an operant conditioning model where the treat must come after as a consequence of good behavior. But what they describe sounds like reciprocal inhibition:

https://en.wikipedia.org/wiki/Desensitization_(psychology)#R...

The idea is that you can't feel opposing emotions simultaneously. So if you can make the dog feel relaxed (by giving a treat beforehand), it interferes with their ability to feel anxiety.

They aren't earning the treat for choosing not the be anxious. The positive emotional feeling from the treat prevents the anxiety from occurring.

This is also an excellent explanation

With Lily we didn't take the risk of bad behaviour during an encounter. We would just ply her with treats and tell her she was a good girl as we walked by a small yappy dog. I think she started associating those encounters with positive emotions.

Thank you! I'm not very experienced with dogs (my partner is) and I'm still too much in my head instead of with the dog. I think I might be trying a bit too hard (or rather too often) to train him instead of just managing situations in a nice way if that makes sense.