I am deadly serious. There has been a successful multi-decade gaslighting initiative to make people think middle class and working class are different when in fact they are both just working to make the investment class rich. Time is your most valuable asset and unless you own it 100% then you are working class.
You're absolutely right in implicitly arguing that social class isn't exactly determined by the amount of money you have.
You're also correct that traditionally the proletariat (the working class) were those who sold their labour. By a very strict definition, anyone who earns a wage is working class and that would include CEOs (as you are doing explicitly). That definition is deficient and doesn't relate to reality.
Traditionally, the bourgeoisie were the class or classes who employed the workers. The capitalists own the capital and capital goods (means of production) that are used in industry. The petit bourgeoisie are those who own small businesses, such as shopkeepers or lawyers. They were middle class because they were neither working class nor part of the nobility.
Today many companies are publicly held. By this, I mean that stakes in the company are sold publicly. Many companies are also part-owned by the public in the sense of state ownership. This kind of relationship would falsely suppose that members of the working class are members of the bourgeoisie. You agree that ownership doesn't exactly determine class since your criterion is the selling of time or labour.
Those today who have power over the factors of production are very often employed when previously they employed themselves. You call these people working class. I find that very bizarre.
I believe that a managing director of an investment bank is a person who represents capital absolutely. Their job is to head an organisation whose aim is to manage capital and to generate or bring in capital in the process. To identify this person with a factory worker is confused.
