I agree that this may be unduely paranoid...
I don't see how you're being unduly paranoid. It's a hardware device and you don't really know what's inside of it. Unless you open up the hardware and look into it (which 99% of the users who claim its trustworthy never do), you are trusting the manufacturer that built this thing.
Worse, you connect this hardware to your online computer via USB! The risks of USB are widely known and have been discussed on this Armory forum before. Again, they say this is fine because the thing inside the hardware that stores the private key is supposed to be isolated. But again, unless you open the hardware (which nobody does in practice), you are trusting the manufacturer.
I still can't understand why people trust this thing. I just don't get it. What am I missing?
In computers, firmware is required to make hardware actually function. While the hardware does whatever it needs to do, it needs firmware in order to actually perform instructions. Since Trezor's firmware is open source, people can audit that to determine that there is no hardware or any part of the software that can compromise their keys (besides bad hardware and hardware based attacks). Even if such hardware was inside a Trezor which could reveal your private keys to SatoshiLabs, the firmware for it would not exist on the device so that hardware does nothing.
Another things is that the people in the company are known and trusted (e.g. slush). The company is registered so if there is a problem with them stealing keys from Trezor's, then users can sue the company and bring about legal action against them.
Disclaimer: I neither trust nor distrust Trezors or hardware wallets. I don't use commercial ones, or any at all. I plan on rolling my own with a raspberry pi at some point.