I mean, object recognition was never an intended way of solving the problem. When you ask for a "frog" image, the model isn't just trying to randomly find a frog object, it slowly narrows down data to find an image that's classified as "froggy". Sure, the actual frog will be remembered as an extremely important part of a frog image, but everything else in the image is contributing too. The background could be something that frogs are photographed in, and the lighting approximates what a photograph may look like.

I don't see why there's a need to explained it with this two-tiered approach (and a "data theft" claim) if the explanation of how it works seems applicable to the entire system. Images in the training dataset would almost always reflect the way lighting and objects work in real life, so the model is incentivized to approximate it as closely as possible.