Exactly, he did not overtake 1st and 2nd during the race, he never overtakes them at all. It is written in the present tense for a reason. The OP is taken from the event as it is happening.
(We must have had a misunderstanding on post #14, it makes no difference if he passed them after they had finished, the race would be over for billy at the point that he crossed the finish line and therefore irrelevant.)
Exactly, "The assumption then became that all participants were overtaken while the race was still going on." Is exactly the right assumption. So, if he never made it past third, yet he passed everyone in the race, then 1st and 2nd could no longer be participants. I never said that he passed everyone during the race, I said he passed everyone in the race, that's the catch.
Again, think of the "as it's happening" situation: (this is not the OP, just the interpretation)
Billy is in last, Billy passes everyone in the race except for 1st 2nd and 3rd. Then 1st and 2nd cross the finish line (they are done and no longer in the race). Now, take a photo. *Billy has passed everyone in the race except for the guy in 3rd.* The OP works this way, and no other way.