I agree that this definition of a hot wallet is wacky. The definition of a hot wallet is easy: it's a wallet that's online and can be accessed by automated systems without human intervention. How you use it is entirely up to you, and nothing says you can't put 100% of your assets in a hot wallet, it's just a really bad idea.
However, I still think it's really odd to only insure the hot wallet and to call so much attention to the fact that it's insured. Imagine if your bank called attention to the fact that they were insured with large, high-rated insurers for any conceivable loss... and then they mention at the end that the insurance only covers what's in the tellers' drawers, not what's in the vault. Personally I'd run far, far away if I saw something like that.
The analogy is tricky, because in many banks the vault is effectively the hot wallet. Most of the money is in the form of debts or loans, and the vault only holds enough cash for normal withdrawals.
It's bad that they have no insurance on the cold storage, but that's something you can't really get anywhere as far as I know. I take it more as a risk of bitcoin in general.
However, I still think it's really odd to only insure the hot wallet and to call so much attention to the fact that it's insured. Imagine if your bank called attention to the fact that they were insured with large, high-rated insurers for any conceivable loss... and then they mention at the end that the insurance only covers what's in the tellers' drawers, not what's in the vault. Personally I'd run far, far away if I saw something like that.