Yes,

You can assert you own or have the rights to those images, based on your license with Adobe.

How do you prove that the images where generated using Adobe Firefly instead of SD or MJ?

They don't seem to be asking for proof.

> we are declining to distribute your game since it’s unclear if the underlying AI tech used to create the assets has sufficient rights to the training data

So it seems that asserting "assets X and Y were generated by tool Z that has rights to its training data" would be sufficient. Presumably AI tools will also start to formalize that declaration alongside their terms of service.

Are there similar things where you have to declare something that is in no way provable in game development? It feels kinda silly.

Yes, its fairly normal for distribution platforms to require you to declare that you have the rights for everything in your game (which is in no way provable), extending it to everything in the training set(s) for the model(s) used for generative AI used is ludicrous, but just amounts to the same thing plus the (almost certainly false) assumption that every work produced by AI generation is legally a derivative work of every work in the training set(s) of the AI model(s) used.

>which is in no way provable

I guess in that sense it's not provable by the platform, but it is provable by the actual copyright owner if you're infringing one.

What I mean before is that no human can know whether you used Firefly or SD or MJ or some other custom model.

Sort of - the person uploading to adobe stock can upload copyrighted material. Adobe will handle copyright claims and be liable up to 10k worth of damages.

Only 10K?