I think the first question is what is your role?
As a teacher, her emotional state can affect her academic learning and her social/peer relationships. It’s logical and maybe even expected that you would want to inquire. It would be a good opportunity to recommend a psychosocial evaluation and maybe even some play therapy.
As a neighbor, your role would be completely different. If you are truly concerned, you could take the opportunity to get to know this family better. Visit them in their home environment. Observe them. Notice the condition of the home, the demeanor of this child and any others within the home, family interactions, the mood of the parents and their interactions with eachother and the kids. Keep an eye out for signs of neglect (filthy home or appearance, lack of interaction or proper supervision, nutritional deprivation (do the kids appear severely underweight?).
There are too many unknows here. Could there be a developmental issue? What is the family history? Have there been any life altering events, such as death, loss of job/income, marital conflict, even general depression within the family context?
You’re also describing inconsistencies. You state that others claim there was no warmth/compassion shown to this child as an infant, however you have witnessed the father being compassionate towards her. Then you state the parents give her everything she needs. How reliable is this information?
I would refrain from making any assumptions, good or bad, at this point. I think it’s more of an opportune moment to get to know her and them before making a decision whether this merits further investigation and involvement.