I think it's a good thing when people care enough about dogs to care if one is being mistreated. it is kind of humorous in a way that the neighbors heard the thwack of the arrow hitting the target, and then the dog howling, and came to the wrong conclusion. But I'm glad it turned out okay for you and your dog.
I shoot with two people almost every day, and we all have dogs. My border collie is probably better trained than I am, and all I have to do is think something and she is on it. Another friend's dog is a catahoula, and is also pretty well trained (no bias here!). They stay with us at the shooting stakes until we move forward. The third dog is a mix of golden retriever and other things. She goes and sits in front of the targets, not for any particular reason, just because that's what she wants to do. Since it is way too late to train her to do any better, we just put up with it until she decides to move on somewhere else. Which might be a while, but that's okay, because we fire too many arrows too fast anyway, and it's good to take a break every now and then.
It sounds like your dog is young enough to train to do whatever you want, including finding lost arrows, if that's what you both want to do. But communicating with another species is not that easy. Compare with communicating with one's own wife, which many of us have difficulty with, and they're supposed to be the same species we are.