Well... actually the BE joined the Horde because they needed allies, and the one who pushed them to join was Sylvanas (as you may know Sylvanas was a ranger general of Quelthalas and for them, she was a hero, who sacrifised herself to fight the scourge, and now she was giving them a way to protect themself, somewhere to go...
Also the BE didn't left Quel'thalas cause Kael told them that he will give them something they could use to fight the addiction and he did, he gave them the demonic crystals (the Green Crystals with shiny yellow eyes that are all around Silvermoon)