To the best of my understanding, ZDR is often a promise that your data is not used for model training. It doesn't mean "what it says on the tin", so to speak. There are cases where data needs to be retained regardless, for example, preventing abuse. This isn't for training, so a company can still claim ZDR.
I'm fairly sure the ZDR on their site impled that neither the prompts or the model output was collected before they've changed their site few dozen times.
They still mention: "meaning they do not store or train on your data", but only on the providers side which makes quite a lot of sense, there's very little reason for them to store anything except some analytics data in cases like these.