If they were auctioning off the same card at the same time, presumably that'd alter buyers' behavior. If you see two Michael Jordan cards up for auction, you're going to notice if one is cheaper and bid on that one. If there's only one Michael Jordan card up, your only thought process is "is this card subjectively worth this price to me?" which I expect would increase the effect of unconscious bias.
Now, they could've done same card at different times, but now you're throwing in the confounding variable of whatever variation the baseball card market experiences over time. Plus you're making the study take longer, and thus cost more.
So instead, they did different cards at the same time. If you randomize which cards are in which experimental group, you can do some very straightforward math to estimate the odds of the observed results being solely due to random chance: if those odds are low, you conclude your experimental variable (skin color of hand holding the card) had influence over the results.
Science.