Dad's dead, mom's working two jobs to pay for the apartment in the good school district, as a result the family only has enough money for the kids to eat highly processed calories, kid is fat, but has a fantastic education that helps him beyond the station of his parents.

This is an outright lie and this is either extremely lazy shopping or stellar excuse making.

Rice and beans and lentils are dirt cheap. Root vegetables and some fruits too. All you have to do is try.

A quick google search: Your excuses are just that- excuses.

And since we must accept that there will always be decisions which are made where someone makes a judgement on one type of harm over another, we can't say "ANY HARM = BAD PARENT"

"Well... it's either I leave my small children alone for eight hours or let Bob the child molester watch them all day..." no. There are seldom situations with only to options.

Now, in that scenario we very well could have an obese child, but the parent has made the difficult decision that she's going to sacrifice his physical health in favor of his mental health.

What? No. "My kid started setting fires, so I beat the SHIT out of him, sacrificing his physical health in favor for his mental health".

Does that make her a bad parent? Or does that simply mean she's making the hard decision which she feels is right given the circumstances?

It makes her a bad parent who is too lazy to actually take time to cook meals, choosing the microwave over the stovetop.

At BEST you can make an argument for ignorance, but I'm pretty sure you're too biased to argue that your mom is stupid.