Last year EDD played 28 games (missing six due to injury) and had 5.3 win shares (per basketballreference.com). Dolson played 34 games and had 2.2. Even if EDD only plays half the time, she's probably worth as much or more in aggregate than Dolson.
She did have back issues in the '14 playoffs. Since the '14 season, she has had no major back problems and no major Lyme flareups that I can recall.
It's not as if Washington would be getting a lemon and Chicago certainly shouldn't let them value EDD that way.
Honestly, I have no idea what you do with both EDD and Meesseman anyway. They have a lot of the same strengths and weaknesses. I guess you play one at 3 and one at 4, but I would think your defense would suffer. Who guards a Maya Moore or Angel McCoughtry in that scenario?