I get what you're saying about the origins of the practice, but I don't even think of walking down the aisle as "giving away" anymore so much as a way to get the parents involved, if one so chooses. Obviously Dick's not a parent, but since Donna's sticking to just having female bridesmaids and male groomsmen for whatever reason, it's nice that she found a way to involve him in the ceremony.
At our wedding, both my wife and I were walked down the aisle by our living parents, regardless of gender, just as each of us had both male and female attendants. We also managed to squeeze "in brightest day, in blackest night" into our vows.