I think this is a very important lesson for startups. Most medium & big companies behave this way. Fix a customers problem, don't make excuses about it not being part of your job, or someone else didn't step up.
Even so, I would expect a conscientious employee to at least make the effort instead. At a bare minimum, instead of saying "That's not my job." they should say, "I am sorry, I cannot help you with that, BUT the person who can is...."
It's a nice example to try to live up to.
"You have the responsibility and authority to handle the customers problem"
I am sure they had been told that in training, but there it was as a daily reminder. Everyone starts a new job with enthusiasm, but I am sure the "I just work here" crowd have been smacked down more than once when they went out on a limb to do what they thought was the right thing.