An interesting idea, but it goes against some of the protections of having a paper wallet in the first place. The paper wallet idea is that the key exists only as a barcode on a piece of paper and has never been exposed to the internet at all. The best way to generate one of these is completely offline on a dumb printer. The best way to use them is as a savings account, and when you do a withdrawal, you pull the entire thing out all at once, transfer the part you want to spend to an active wallet, and put the rest back into a new paper wallet.

With this, your private key is probably seen on the internet at least once when it is created, and if they were unscrupulous they could store it there when that happens. Also, every time you spend money it has exposure to the internet. This is where the unhackable thing falls apart. If someone did get into their systems or into the system you use to scan your private key paper wallet in, then they can spend anything that you don't use from your wallet in that transaction.

So, if it's legitimate, it could be a slightly more secure version of the current online wallets. If not, they could be accumulating private keys until they get enough stored up that it's worth filching them all. The only way to be sure it's the former and not the latter would be offline generation of the paper vaults.