Help

I learned grammar by the seat of my pants, which is to say, I have strong opinions about what is wrong and what is right, but cannot quote the rules (I went to a school which, in addition to teaching the New Math, taught the New Grammar). So am I insane to be bothered every time I hear the Stanford Medical Center radio ad which features a sentence that goes "Both saw specialists that diagnosed and treated them..."

My ear says "who." Am I insane? I mean, I could be, I'm willing to entertain the notion (it's Stanford, after all, and someone there must have had the Old Grammar).