You are correct, the study's analysis is flawed.
You are on the right track think it is purchasing power that matters. You are also right it in includes too many rich people as middle class.
I would suggest the right formula would be to rank families in quintiles based on purchasing power.
Bottom Quintile are poor
2nd Quintile are working class
3rd Quintile are middle class
4th Quintile are upper class
Top Quintile are the rich.
I don't have purchasing power data but just raw income the break points for the quintiles are
This puts middle class income ranges at $50K to $80K.
The distinction I make is a class called upper class that people like to call upper middle class. That is just a name game to hide the fact that those people are more than comfortable. Currently the U.S. middle class is comfortable and working class is precarious. Upper class is luxurious.
Adjusting for purchasing power does not really change the quintiles just who would be in which quintile depending on their cost of living situation.
I recommend against the open house. I do think that is flaunting. Not so much that you are showing off your house but because you are having a big party to show off your house. I think the right thing to do is have smaller dinner parties starting with your closest friends.
This all could be completely biased as we live in a low cost of living area and my income is in the top quintile, my wife does not earn an income, we don't drive luxury vehicles, we did buy a new house and that made her family jealous. We don't host parties not even small ones. What do we do with our money? We invest it. Why? What else to do with it. We have more than we want.