>Are the students doing poorly in those schools because they are poorly run/staffed/and funded, or is it the case that the students in those schools have more problems at home leading to poorer results?

There has been research (don't have it handy right now) that there's a negative feedback loop with that.

Schools in poor areas tend to have less parental involvement (and direct economic support from those parents as is common in wealthier neighborhoods), so school staff don't have as many resources and aren't as incentivized to raise expectations of the students.

That creates an environment where the students aren't learning as well as in other neighborhood schools.

I suspect that if the authority figures on either side of that raise their expectations and requirements of the students, the negative feedback loop can be, at least partially, short-circuited.

>In other words, is this a problem schools can fix at all?

Yes. They can't do as much as schools with significantly more parental involvement, but improving the teacher/staff performance would likely improve parent performance.

No, it's not a panacea, but blaming all this on poor parenting and throwing up our hands just promotes the centuries-old trope that "poor people are morally and intellectually inferior. It's obvious, if they weren't so they wouldn't be poor."

That's circular reasoning and doesn't reflect reality.