Yes, she was fairly terminated. If she wanted to do that, she should have cleared it with her employer first. The specifics of her job don't matter, so I won't delve into that there could be scheduling, safety or legal issues with what she did.
She was hired to work a specific shift, and she unilaterally adjusted her shift because she thought it was fair, without knowing the implications of her decision, and not discussing it with her employer.
This is cut and dry.
Coincidentally, one of my workers has to leave 15 minutes early 3 out of 5 days during the week because of her childcare needs. I gave her options of either taking 15 minutes off one of her breaks, or simply not getting paid for those 15 minutes, and she opted for the latter. All good! If, on the other hand, she just started disappearing 15 minutes early without a word, I'd be giving her a talking to, even if she had been taking 15 minutes off one of her breaks voluntarily. I mean, think about it. What if there was a fire and we couldn't find her? We could potentially be sending rescuers into a burning blaze to save someone who is safely at home with her kid. That's just one possible implication.