If the ticket was obtained illegitimately (i.e. stolen, as you suggested, or even lost and found) the authorities can likely determine that by seeing where it was purchased, where you were at the time, using possible video surveillance of the ticket vendor from the time of sale, etc.
Stolen would surely be unlikely to get away with. Even a found ticket it is questionable if it would be honored, and indeed unlikely if they realize it was a lost ticket.
But you’re correct that there is no ID required at the time of purchase.