Anecdotal obviously, but mine made no such attempt. I was reminded constantly of our financial situation and furthermore, was normally informed through various means how it was my fault for one reason or another. Yay.
Looking at the study I also wondered why they chose something as controversial as real money.
That the response to rewards differs between poor and rich in general does't seem to be testable using a reward that both groups perceive differently.
I was eventually removed from my parents through the assistance of the courts and my grandparents who were witness to the significant mental and physical abuse I suffered at the hand of my parents. They had to spend the remainder of my youth/teens attempting to reverse the idea I had gained that everything that occurred in life of a negative nature must be inherently my fault, and the behavioural issues I had picked up resulting from that. By explaining that adults make choices, choices I cant be held responsible for when I had yet to even be born, etc etc. How successful they were is debatable because even into adulthood I've a tendency to assign blame/accept blame when it is apparently unwarranted according to those around me over the last couple of decades.
Aka my first assumption is always "this must be my fault in some way." even if I can not see an immediate manner in which that could possibly be true.
For context; my parents were actually poor because my mother never finished school, fell pregnant with me at 15, made poor life choices and her and my stepfather pissed most of their money away on cannabis for the duration of the time I was raised by them. Cannabis first, everything else later, if at all.