Hardware wallet question.

So hardware wallets supposed to keep private keys safe by keeping them off the internet.
The way I understand it : These wallets keep private keys compartmetalized, inaccessible to anyone from the internet.

So how come If I lose or damage my hardware wallet ,I can restore it with my 12 or 18 word back up phrase?
Doesn't that mean that it is backed up on the internet in some form?

Please help me answer this question?

Thank you!