I'm convinced that yes, accounts can be flagged for certain (unlucky) moves.
Here's my luck of note, which illustrates how frustrated I was pre-TM. I had actually sworn to quit the game but they announced TMs the very next day.
12 Rhydons. 2 got Mud Slap and the rest Rock Smash. I recently TM'd one to get 3 with MS to counter Raikou.
8 Dragonites. Every. single. one. got Hyper Beam.
8 Charizards. 6 got Dragon Claw.
12 Gengars before the moveset changes. Only one got Shadow Claw/Shadow Ball, and it's a 73% with 4 attack.