I would exclude the 1900 motoring events, given those Games were utterly hopeless and nobody knows what was really included. Only motor event that really counts is motorboating in 1908 as that was specifically included, rather than retconning after the event. Especially given that many of the chauffeurs were professional...
Go ahead, be my guest, but like it or not, the record is still the record. Until I read this article in the journal that focuses exclusively on the Olympics, I was quite puzzled by the inclusion of automobiles in the 1900 Paris Exhibition (re: "International Athletic sports and Contests at the Paris Exhibition of 1900," The Nineteen Hundred Paris Exhibition Illustrated, Vol. 8 No. 3 (15 March 1899); and the report of the Ministry of Commerce, Industry, Posts, and Telegraphs in 1901 on the "Exposition Universelle Internationale de 1900 a Paris" (two volumes) which addressed the events in Section VII, "Automobilisme." Not to mention the various reports in the automotive journals of the day. It is still something of a puzzle, but the events certainly did take place in conjunction with the Exposition or Olympics. Then again, I tend to keep Gordon Wood's worlds in mind regarding events from the developing years of motor sport: As Yogi Berra might put it, it is difficult to write history, especially about the past.