Marianne, your Class B permit is for indirect sales, and I think this would qualify for that, as long as the person selling it is doing so within your county (or in other approved counties, where the necessary agreement with the health depts exists). Indirect sales usually happen at food facilities or grocery stores, but it also includes someone who sells your product at a farmers market.
The person who wants to market your goods should have the necessary licenses before doing so, but they still need to be aware of the limitations of your Class B permit. The label on the product needs to be your label, not theirs. It needs to have your business name and address (unless your address is in the phone book), and it also needs to have the other requirements, including your permit number and the disclaimer about the product being produced in a home kitchen. You said that it is their product, so maybe they wouldn’t be okay with that. They also should be aware of the sales limit you have, and that once you hit that, you won’t be able to produce their goods until the next year.
Maybe the reason why AB 1616 doesn’t really cover this use case is because it is unlikely that a business would want to go this route, given the limitations of the law. The cottage food law is really intended for people who are testing their food business concept. But in short, I think this arrangement would be legal if the seller is aware of and abides by the limitations.