I have noticed that some Chinatown restaurants don't tend to identify themselves when I call in. I think part of it is a language / cultural barrier. It's a lot different calling a chain where they have huge manuals on how to interact with customers vs an immigrant family run business. Is that not the case for your Chinese restaurants?
However, more likely I think they edited out the initial introduction to give the businesses privacy. They also probably told the businesses beforehand that there was a chance they would be calling in the future with bots to get around California 2 party laws on recording (or maybe they got approval afterwards although I'm not sure that's legal).