To me, the lower class is defined by anyone who depends upon someone else for theirs or their family's survival.
The upper class are those who make money work for them and, if necessary, could live from this income.
Everyone else is in the middle class.
You're explaining the symptom of not making enough money. If someone only makes $10,000 a year, they'll be dependent on someone else because it is very difficult to live on that low amount of money (in the US at least). That's why people use numbers, because it's a way to measure how much one needs to be a certain level of dependency year over year.
By your rationale most retirees are "upper class" because they live off of their investments (i.e., 401k accounts, etc.). They could only get $35,000 a year in income from those investments but because they don't work to create that income you'd call them upper class. They have to live on a strict budget, have little extra money to have the freedom to do things, yet you'd call them upper class. On the other end of the spectrum you have the stereotypical single mother of a few kids working three jobs to make the same $35,000 a year, living a very meager life to provide for kids on this small income and you'd consider them middle class. This is where your logic doesn't pass test for me.
I think your logic is good for another assessment. Maybe it's an "independence factor" or a "contribution factor"...the less dependent you are on others the more independence you have or contribution you make. I don't think it's a measure of economic class.