At the end of the week, the top 100 all go into a lottery with presumably equal chance. 12 names are drawn out, and the CR's are distributed in order of score (ie. highest score gets most expensive, lowest score gets least expensive).
So yes, if you place exactly 100th you will have an equal chance at receiving some sort of CR as anyone else in the top 100 - however placing 100th will only ever get you a chance at the lowest prize as everyone else drawn will be above you in score.
I imagine a lottery, where 12 random numbers from 1 to 100 are drawn, and the prizes are awarded to players whose rank matches that number, and the prizes are awarded, in order of rank. So the top guy gets the best Cr, the bottom guy gets the worst. Sometimes, the Crs are not ranked in order of price. For example, it is possible that the 7th Collector is worth more than the 6th.