Seems that they don't know exactly what is private key or they have another definition for the private key.
They do seem to define "key" differently to what we are used to, and are quite vague about the whole set up. I did, however, find the following snippets from their FAQs here:
https://support.bitwala.com/hc/en-gb/sections/360000146580-Bitwala-walletBitwala wallets are secured through a 2-out-of-3-multisignature key mechanism.
The main key and the backup key come in the form of mnemonic phrases that must be written down on paper and stored safely.
Each wallet has three keys. Of those three keys, two are required to use the wallet. The main key is generated upon choosing a wallet password in the first step of wallet creation. The resulting main key seed is only presented to the wallet creator and must be written down immediately. Afterwards, the second key, the backup key, is generated and must also be written down by the wallet creator.
The third key is the BitGo key which is generated and securely stored by BitGo. Neither Bitwala nor BitGo has access to your wallet.
So when you generate a wallet, it gives you two mnemonic phrases (which they are confusingly calling "keys"), which you are supposed to write down and back up like you would with any mnemonic phrase. The wallet is a 2-of-3, with you holding 2 keys as backed up mnemonic phrases, 1 of those 2 keys within the wallet itself when you log in, and the other key being held by them. So it
is a 2-of-3 multisig between yourself and them, but at the same time, by using your 2 backed up keys you also have complete control over your coins if you wish.
You will still, then, be able to sell your bitcoin elsewhere and send the fiat to your bank account, but the big selling point of their set up seems to be that all the intermediary steps happen automatically - you sell your bitcoin directly from your wallet on their exchanges, and the fiat automatically appears in your bank account, ready to be spent. No extra transfers or waiting several days for the fiat banking system to play catch up.