In many years of doing this type of work, I've noticed this fear of your neck being on the line is a myth. Heads rarely roll merely because something goes wrong.
I've also noticed almost every sysadmin believes that myth, and it can make us very difficult to relate to or even work with. Ironically, that's a problem that may actually cause you to lose your job.
Usually you can trace the insecurity to mismatched assumptions, unhandled edge cases or a failure to consider global contexts (like where you accidentally turn one function into a decryption oracle for another).
A problem shared is a problem halved. In this case every web developer needs to have a network of people to collaborate with in order to diagnose the problem.
Open-Source software has bugs, but it gives you the ability to look into the issues directly; allowing you to figure it out if you want.
The cool thing in open-source is you can always absolve yourself of responsibility and hire a vendor or maintainer or others to help fix the problem if there is one. Which means you have N potential solutions to a problem, compared to just 1 with a closed source vendor.