Loyalty has nothing to do with learning moves. After I hit 70, having used a pet boar and ONLY a pet boar since around level 30, I went out and learned all the highest rank moves for every other pet.
Every one, and I do mean EVERY one, I learnt on first use.
I realise this isn't the case for everyone, but it should be enough to prove that you don't need to go and grind a pet prior to learning a move. Highest ranks of Claw, Bite, Dash, Dive, Screech, Lightning Breath, Prowl, Cower, all learnt on first use, directly after taming mob.