Didn't Snape actually do something for Dumbledore, namely spying on Voldermort 'at great personal risk', that made Dumbledore trust him, not necessarily DD 'reading his mind'! Or perhaps, he did both, to be sure !
By the way, Snape has the legilimens ability, because that's what he was doing with Harry! He pried around his mind and thoughts while Harry had to close his mind to that.