I see this every damn time someone hits multiple home runs in a game (congrats, JD Martinez). Everyone complains about how they’ll get “random” drug tests, and it’s clearly not “random”. It happens every 4/20 too.
Here’s the answer: it isn’t meant to be random. “Random” only applies to the player. The MLB (and NFL, and NBA, etc.) Have the authority to do it *randomly (I.e. at their discretion, without warning the player in advance) as a way of potentially catching a player in the act of cheating. It’s to deter people from cheating. It isn’t random for both sides because there would be no practical benefit for that.