The burning of gas fees

Ledger says this about network fees:

Your maximum transaction fee is equal to gas price x gas limit. Once the gas limit is reached, you won't spend more and unused gas will remain on your account. On the contrary, if the gas limit or gas price is not enough, the network will still burn your fees trying to process the transaction but eventually, it will get dropped by the network and the funds will remain on your account.

Is this true?

I thought you can lose your fees if you set the gas limit too low.

But if you set the gas price too low, your transaction is left unprocessed and maybe dropped from the pool eventually, but no fees are burnt because no processing happened.