[MeteorMiss]

Originally Posted by Fat Zowayix

Technically there is one way to get a Pokemon with an ability it's not supposed to have.

Red-Striped Basculin are supposed to have either Reckless or Adaptability, with Mold Breaker as the hidden ability.
Blue-Striped Basculin are supposed to have either Rock Head or Adaptability, with Mold Breaker as the hidden ability.

However, in BW1 only, wild and hatched Blue-Striped Basculin accidentally draw from the the Red-Striped ability list, making it possible to have a Blue-Striped Basculin with Reckless. This situation is identical to a hacked ability, as Reckless is neither the primary, secondary, or hidden ability for a Blue-Striped Basculin.
In fact, the only way to properly get a Blue-Striped Basculin with Rock Head before BW2 is through that one in-game trade, which hardcodes the right ability instead of (improperly) calculating the ability from the personality value.

So yeah. It's a pretty extreme corner case from a glitch, and not too useful competitively, but it technically exists.

It seems more likely that both formes of basculin are supposed to have Reckless, and the in-game trainer was the mistake. I'm pretty sure the standard ability list is the same for both.