I have watched biters & had one of my own be a biter. This is what has helped me most.
Firstly, for me the only biters I had were non-talkers. I think this is very normal from speaking to others, researching it myself. It really is a communication. It might be one we do not prefer, but it is a communication/expression.
It is more useful to stop biting on the whole if you can stop the child before the bite is landed. The more a child lands a bite successfully, the more ingrained it becomes as a way they go about life & getting through their own frustrations. So the key then becomes observation so you become better at predicting "bite-likely" situations so you can intervene before anyone is bitten. This isn't easy. I am aware, as in a day there is a lot of reasons to miss the signal, like cleaning up spills, grabbing something you need, picking up toys, etc. But you do the best you can do & watch everything.
I find a loud noise is a fast interception to a bite when you see one coming. So a loud "HEY" really quickly, a clap of hands, etc. It will often startle them into stopping what they are doing to look at you. Then you can intercede & tell them what else they can do. "When you are mad, you can stomp feet" or something you find an acceptable alternative that is non verbal & within his capacity, so he can feel able to express his frustration, anger, etc without doing something you don't want him doing.
You can at that time also offer things you can bite. My one who is a biter does want to bite, period. It helps her ease frustration. I have chewelry for her, it's actually meant to chew, for kids. She also can opt to bite on a stuffed animal, a blanket, a pillow, and she will sometimes choose to do so. That is fine. She also is allowed to scream into pillows & likes that too for now. It helps give her tools on acceptable ways to deal with her own feelings.
If a bite is landed, pay no attention to the biter initially at all. Always rush to the aid of the bitten child, lavish them with attention, make sure they are okay. Be a bit dramatic in the "OH MY GOODNESS YOU POOOOOOR THING!" and lay it on thick. Generally speaking, the biter doesn't want you to adore the person he/she was so irritated with, so that alone is a deterrent. When the bitten child is all better, you can then say, "We can bite (insert whatever you want him to have) when we feel like biting, but we don't bite people". Keep it simple. He is too young to retain anything longer than that.
Really though, this is handled on a core level like all aggression in young children. You just offer then other options, take care of the "victim" FIRST before addressing them & then offer the thing you want them to do. Just saying no, or punishing will never work because toddlers are not problem solvers. That bite is a release. If you do not offer him something else to do instead when he feels that way, it will take a lot longer to address it. If you merely say "don't do it" on whatever it is, that doesn't help them to sort out what you want from them. So when this age, all day I spend saying things like "Here, THIS is a better item to play with. How about we push the buttons on this toy? Let me trade you this, it's so much MORE fun than the remote. You want to climb? How about me make a pile of pillows you can climb then? Oh I see you are sooooo angry right now, how about me bite on THIS to let it out?" That sort of thing. I reduce "no" to absolute minimum (helps avoid frustration) and I offer great alternatives all day to try to keep them within the limits of what is safe, appropriate & good without constantly having them feel like every time they turn around they are being told they cannot do or have what they want.
I also think your response to the parent(s) was very thoughtful & professional. All children will run into being bitten eventually. It really is quite normal for age & I am not sure why people get so upset about that one thing in particular. To me I prefer my kids do not ever cause pain to other kids & likewise I prefer other kids not cause pain to mine. That said, it is bound to happen among toddlers in particular & all you can do is manage it, teach through it, and keep an eye. It sounds like you are doing that.
