I used to be a web freelance web developer/tech guy with one client, a designer. What made me quit was an incident where his client's Wordpress site hadn't been moved properly to the new hosting. (not by me)
The DB needed to be searched and replaced to remove all the old urls. After doing so, the wp_options cell on the production site holding much of the customizations kicked back to the defaults for the theme, the serialized data format being used was sensitive to brute DB-level changes.
I had talked to my client before about putting together a decent process including dev databases, scheduled backups, everything needed to prevent just such a screwup, but he waffled. Then blamed me when things went wrong.
I'd had enough and told him to do his own tech work, leaving him to fix his client's website himself. Being that I didn't build it, I didn't know which settings to flip back. I left freelance work and never looked back.
People and companies do this all the time, refuse to spend the time and money ensuring their systems won't break when you need them the most, then scapegoat the poor little technician when it does.
I'd like to say the answer is "don't work in such environments," but there's really no saying that it won't be this way at the next job you work, either.
I certainly wouldn't internalize any guilt being handed down, ultimately it's the founders' jobs to make sure that the proper systems are in place, after all, they have much more on the line than you do. Count it a blessing that you can just walk away and find another job.