If you bought every single song and you have a proof ( email from beatport for example ) , you can dispute claims without any problems .
When you buy a song from beatport or similiars , you buy the license to mix it and play it to the public .
It used to be like this few years ago . I don't know if they changed something but when I used to mix , I didn't have any problems with my DJ Sets .
If you don't have the proof , well , it's going to be removed .
As I said , beatport gives you a written permission/license .
That's why songs are that expensive .