People do make false accusations. But you know what is a lot more common than that in the world at large? Actual discrimination.
The problem is that most of the time Person A discriminates against Person B, Person A will swear up and down they have done nothing wrong and had no ill intent. That is what makes it such a difficult issue and one where people need to be open minded when hearing from people who do not share their life experience or social status.
It's a lot more healthy and beneficial in my view to approach any complaints with an open mind. Obviously in the end we have to try to come to terms with the facts, but when you put up a bunch of barriers before a victim can even be heard you are protecting the status quo. Which probably sounds great if you are a person who is really comfortable, but might not be so great for someone else.