Where's the case?[0] I also don't see the point of lowering the temperature of a plastic battery lid. It's an insulator. I guess it would keep dust off it, though.
[0] https://d3as1itr0z6zbr.cloudfront.net/assets/marketingConten...
[0] https://d3as1itr0z6zbr.cloudfront.net/assets/marketingConten...
As to why the lid should be in the fridge? My real-world guess is so all the bits are in one place, but the real reason is likely because the audience will more easily recognize the top of a battery over just seeing the chemicals.