This mare I caught wild.

Training stats when caught should have been 333333. As all wild horses stats are to start with.

Trained 4 times and her training stats are 222222.

this is a bug.

Thanks:

QHTB

Some horses have weak trainings and buttons can go down during training.

This does not seem to be a bug.

She also looks like a starter horse, she was captured on the day you created your stable, and is rated PPP with no crazy patterns.

Why do all the other wild horses have stats at 333333 when captured? She only has 222222 after her training.

Starter horses are "captured" with stats at 222222. As Kuewi said horses can have weaker training and not necessarily gain bars on wk 4.