How would you define a genuinely nice person?

I would not say that most people are genuinely nice. I would say that most people act nice when they are first getting to know you or if they want to impress you for some reason. Then as soon as you say or do something they don't like, they turn on you pretty quickly.

People who are willing to look past your obvious flaws and problems and who still want to befriend you in spite of those things. That to me is a genuinely nice person.