http://www.bbc.co.uk/sport/0/football/20866989 Sheffield Wednesday player gets booked twice, but no red! Also, the second yellow came after 26 minutes, that's rather quick!
Apparently the first one was for diving which should have been a penalty! Perhaps he was trying to atone for his error!
Also, had the player who was wrongly booked to begin with then received a second booking himself, and therefore sent off, then he would have felt rather hard done by. But I think you can appeal on the basis of wrong identity.