How much can we trust using Trezor?

Got my Trezor in the mail yesterday.. got it set up and must say.. finally getting my funds off Coinbase was a liberating feeling. But it also got me wondering.. I understand the principles of using a hardware wallet, but don't the same security risks people face with coinbase exist with using a Trezor? What's to say SatoshiLabs goes under and you are no longer able to access Trezor Wallet web interface? I understand you can use other wallets or python to secure your keys yourself but the process of moving my coins over to the Trezor just had me wondering how much more safe it is trusting someone like SatoshiLabs as opposed to Coinbase.. I'd rather trust no one but myself to be quite honest.
Essentially if there are any other Trezor owners out there, i'm basically looking for advice and information on how to best utilize the hardware and secure everything myself without having to rely on a third party like SatoshiLabs.

EDIT: Thanks for the info guys, much appreciated! Can't put a price tag on peace of mind