As an international calibre cyclist, Sáblíková has long harboured the dream of competing in the Olympic time trial event at the 2016 Summer Olympics in Rio de Janeiro. After finishing 12th in 2015 in the women's time trial at the UCI World Road Championships in Richmond, U.S. (9th in the reduced rankings), Sáblíková was thought to have secured a place at Rio 2016. However, when the UCI published the list of nations that had qualified for this event at Rio 2016, the Czech Republic was not among them. The UCI used an interpretation of the qualification rules where an athlete also has to qualify for the road race. She decided to travel to Rio in the hope that the decision might be overturned, but did not compete.