Earlier quoted context omitted.
I use signs (not ASL) to communicate with my dog. When she was a puppy, she was having trouble learning verbal commands, so I started pairing them with unique gestures, which worked much better. Eventually, I mostly dropped the verbal part and now we just use gestures. Her vocabulary is small (she's a dog), but we have gestures for e.g. "sit", "lie down", "stand back up", "stay", "come here", "go there", "be quiet",…
I suspect that at least some dog owners who think they've verbally trained their dogs have actually trained them (and the dog has trained the owner in return) based on body language and gestures they don't consciously know they are making, or at best through intonation rather than actual spoken command words.
My dog intuitively knows just about anything I could want her to do. She follows me (or my SO if they're home) rendering commands like "come" irrelevant. If I put on pants during the day, she idles back and forth between where I am getting ready and her kennel, finally opening the door herself when I'm ready to leave, then I latch the gate.
She has a pretty consistent schedule so most of the time, when we're doing something, she knows exactly what her role is. Another great example is treats. For the longest time we only made her sit to get treats, so now she basically does that. A few months ago, I wanted her to learn lie down but I paired it with sit first. So now if she hears the treat bag, she'll come over to me, wait for me to say one word, then she sits, then waits for another word, and then she lays down. However those words are meaningless to her. If I say, "Lay down" first, she sits. You get the idea!
That said, she's a great pup and very well behaved. :)