buying a hardware wallet does't mean your coins are safer. that's right. i was planning to buy a trezor but didn't do so as it is not offline.
that's why i bought a few thumb drives to store my backups. that's really offline as they are not connected with the net.
I am no expert in trezor, but as far as I have understood the trezor system, is that the whole point that tx signature done on the trezor device, and the private key is isolated from the usb interface.
The application running online have at no time access to the private key, thus making the private key offline all the time.