Ultimately, if a bug in a library causes issue with your program, and your company loses $X, your superiors will not give a shit. You have the burden of responsibility for the program.

For common major libraries used worldwide in enterprise products, you are right in that there is an element of trust. They are made by people much faster/better/stronger than most of us. If all else fails, the sheer magnitude of people using it is a small insurance policy, as disastrous issues will probably be quickly apparent. That still doesn't absolve you of responsibility, but the overall risk is usually pretty low.

A segment of code on SO, or a weeny niche library? You only have your noggin to vouch for its stability and accuracy.