No, few "good" landlords don't do credit and background checks. There are plenty of idiots and slumlords who don't run checks. They also don't fix things, take pride in their buildings, or keep criminals from living in the unit next to you.
I rarely do background checks except on the people who actually make it through my screening process. I catch a lot of lies on the application and can deny them without spending a dime of the application fee. Those people I call "Easy Money".
What others have failed to ask is what was the difference between what you thought the rent was and what the LL thought it was? Why is there the conflict to begin with?