I think it's relevant to note that 'the poverty mentality' and 'being in poverty' are more of a venn diagram situation than they are different descriptors of the same thing. Take an example of a motivated / hard working / financially responsible poor person who climbs out of it and gains financial independence vs someone who always feels like they're going to be stuck in poverty no matter what, so why not just treat themselves when they happen to have the money for it.
You are right, they are overlapping things that are different. To break out of the poverty mentality requires insight and education. To break out of the poverty situation requires action.
We all know what happens when a person with a poverty mentality comes into sudden wealth but does not break free of the poverty mentality. He or she loses that windfall and ends up right back where he or she started.
Breaking out of the poverty mentality is relatively easy; all it requires is exposure and insight. As Milton said in "Paradise Lost," the mind is its own place, and in itself/ Can make a heaven of Hell; a hell of Heaven. Changing our mentality is a purely internal process, but the situation we have involves the behaviors of not just us, but the people around us to whom we are connected. They can pull us up, or allow us to lean against them for a while as equals, or pull us down. "Up" and "down", by the way, are relative terms. Each group has its baseline, which is a function of the group's values and behaviors. People within the group tend to be pulled toward wherever that bell curve is centered. The behaviors of people with a poverty mentality pull down a normal and functional person who operates at the mainstream middle-class level; the behaviors of normal middle-class debt slave people pull down a person committed to FIRE. Trying to rise to a higher level, when the people around you are not also committed to doing so, feels like being a crab in the proverbial barrel.
The means by which another person's emergency creates an emergency for us is the strength of the tie that binds us to that individual. When an individual is attached to someone who is self-destructive (and the reason for self-destructive behavior varies) the behavior of that attached individual can create an indirect financial emergency for an otherwise functional achiever. Anyone married to a compulsive gambler or serious practicing addict can explain just how easily it is for the responsible partner to be held legally and financially accountable for the self-destructive partner's binge behavior. If an otherwise functional person is emotionally enmeshed with a self-destructive person, then the emergencies generated by that individual's self-destructive ways are so troubling that the pain caused by sacrificing one's savings, or by going into serious debt, is less painful than watching the self-destructive individual experience the predictable consequences of his or her behavior. The only way to not get pulled down is to cut yourself free.
I hope none of us really expect the values and behavior of other people around us to change just because the contents of our own minds and pocketbooks do. That's not how human minds or values work.
Those of us who escape poverty and achieve functional adult independence, or who move beyond functional independence and achieve FIRE, are either surrounded by people with similar values and goals to start with, or else we achieve the minimum necessary level of physical, legal, financial, and emotional separation from people whose needy and chaotic behavior would otherwise drag us back down. Hence my scythe.
Separation is easier said than done because humans are social animals who start out dependent on other humans. It's not always easy or even possible to walk away from dependent minor children, a spouse you love, or a parent who is in need. If you have resources, or the ability to borrow, the desire to help a sibling or relative in need is often overwhelming. Make enough decisions like that, and take the hit for enough non-functioning adults, and it becomes impossible to save enough to invest. When someone close to you creates a crisis, sacrificing your savings and investments or taking on debt are painful, but the emotional consequences of *not* taking doing so are worse. I don't claim to have always been immune to this myself.
TL; DR version: if you're enmeshed with an adult who isn't functioning, it's often impossible to accumulate wealth. But it's sometimes possible to buy a truck.