My parent did not say "labor class" (a mishmash of words), they said proletariat, which is an abstraction that has a real history. Most of us here are petty bourgeois, labor aristocrats, or settlers. A house or a 401(k) are literally capital. So, the proletariat is defined by utter poverty more than being wage laborers, yes. That's my point. Those conditions of utter poverty define the majority of the world's population, but exceedingly few in the imperialist sphere.
I mean, the wikipedia on proletariat disagrees with your definition: https://en.wikipedia.org/wiki/Proletariat
The proletariat’s primary economic value is their labor. They do not own the means of production. Having capital is not the same as being able to live entirely off your capital and the hired labor of others.
In Marxist terms, we are possibly the petite bourgeoisie, although I personally always viewed that as being only the small-business-owning or freelance-style non-capital class: i.e. people who don’t live off their money/property exclusively, but who own a business that they themselves must work to maintain. People who “are their own boss” but who still have to work, essentially.
A key point is that the petite bourgeoisie always wants to act like and identify with the capital class, despite not belonging to it. In an era of continuously deepening equality, the petite bourgeoisie would likely be better off identifying more with the proletariat, since the capital class is not itching to let them in.