The dead ringer expression may indeed have evolved the way the site suggests, although this researcher seems to prefer another derivation.
Ringer: A "dead ringer" for someone is another person who has a great resemblance to that person. The word 'ringer' originally described a horse used to illegally substitute for another in a race. Why 'ringer' is used has almost defeated my researches; one possibility is that the word, which was once slang for 'counterfeit', was derived from the brass rings sold as gold at country fairs. 'Dead', in this instance is used in the sense of abrupt or exact, like in 'dead stop', or 'dead shot'.
An alternative explanation comes from medieval times. In order to make sure that a buried person was actually dead, a string was sometimes tied to the deceased's wrist and attached to a bell above ground. If he was merely unconscious and woke up, he was able to ring the bell and draw attention to himself - he was a 'dead ringer'. Personally, I don't like this one much, as it has little to do with current usage. However, it could still be the basis, since it has been suggested that someone having a close resemblance to a deceased person was regarded as being the 'dead ringer'.