There is a question of how you would know if the holodeck was recreating the ‘67 World Series inaccurately. It can match all the historical data available, audio/visual recordings, newspaper reports, personal reminiscences, ticket sales and employment records, but you don’t know what you don’t know.
Maybe as a publicity stunt, a holopublisher could send some sort of probe back in time, or build a specialty super-sized optical telescope positioned however many hundreds of light years away to record an event “live” and compare the 24th century scan to their reproduction, but that seems like an excessive commitment to authenticity for anything short of a forensic examination where there are real consequences to the smallest detail of what’s depicted.
Though, we saw that exact case (both cases, really) in “A Matter of Perspective,” where the holodeck had the blueprints of the science lab, and the physical profiles of all the people involved, and animated them to dramatize each witness’s pre-written statement.
