R.E.N. Spells Ren
Veteran
It was actually really good writing. When Stannis said "duty" Brienne remembered her oath to Catelyn. Whether she left him for dead, or took him to use later is immaterial. The takeaways from that scene are that Brienne realized her true duty was to the Stark children, Brtenne realized her quest to avenge Renly had caused her to neglect that duty and that Stannis is alive.
No, that's not immaterial...she spent the last 3 seasons vowing to avenge Renly. As I pointed out before, she only entered into Cat's service under the condition that she'd still be allowed to kill Stannis
Leaving him to die makes ZERO sense, as finishing him wouldn't stop her from getting back to her duty of protecting Sansa (unless she NEEDS Stannis, in which case she wouldn't leave him to die)