Therefore, to behave with integrity, you must have formulated your own set of values about what is "the right way" to behave.
Every minute of every day, we all have the option to behave with or without integrity in a whole range of ways.
You earn respect by demonstrating behaviours over time where you have taken the interests of others into consideration, generally people consider someone who behaves like this to have "integrity", especially when they continue to behave that way when no-one is looking.
Saying things like "The ex-admin's bosses probably thought they were the important ones" indicates a childish set of values where there is a power struggle between employers and employees ........ of course the "bosses" are the important ones, they act for the business which is an independent legal entity, upon which many people depend for their lives to work effectively. If, as an employee, you feel poorly treated or otherwise dissatisfied, then the right thing to do is leave in a polite and respectful manner, even if you feel you were not treated in that way. Depending on the circumstances, if you were actually treated really badly, then the right thing to do is pursue your complaint through the appropriate legal channels.
Someone important in my life once said to me "the only thing you have is your reputation". Take that reputation, defend it, enhance it, nurture it and earn the respect to grow it. Don't throw it in the garbage by smashing other people (or their business) in a childish tantrum. I admit this is hard to do - I regret many things I have done in my life, but I try to lead a life consistent with my own sets of values that I think are meaningful and I get rid of people from my life who I think don't have integrity, or whose values are different from mine in critically important ways.