It's not a trivial bar to clear, if you want to own the means of production that happens to be a viable livelihood.
If the means of production is now a livelihood, I have to say that this is a great example of how "means of production" is an insufficiently-precise phrase. It means all things to all people.
Marx seeing his mate's factory and thinking "it'd be nice if the workers owned that" and coming up with a generic-sounding equivalent phrase isn't really good enough to define a real concept.
Which is why people who use the phrase "means of production" seem to all mean different things. Owning a hammer is owning the means of production. It's just the means of production isn't enough.
In a carpenter's hand, a hammer is a mean of production. Whereas owned by someone incapable of producing what can be considered work of carpentry, it wouldn't be.
If the phrase refers to literally a tool which that can be used by some arbitrary somebody --- not necessarily the owner --- to produce something, then we're all in possession of "means of production", by simply having a body with basic I/O, which enables us to be a freelance CEO.
I find that to not be a very practical definition, and probably not the meaning used by whom your first reply was directed to.
Even Marx agreed that people have access to some means of production: the carpenter owns the hammer. However, after capitalist development, the major means of productions that produce the majority of wealth (like the industries that produce most GDP for a country) are indeed outside the reach of most people and this creates a division between people who gets money because they labor and people who gets money because they own capital and relevant means of production.
I'm always fascinated by this sort of thing. What do you mean "after capitalist development"? Do you think once upon a time people owned factories together, and capitalism came along and stopped all that?