Agreed. That's why I was pulling up bank statements last night, because I wanted actual data.
Define necessities -- food, shelter, health insurance premiums, and I'll even throw in child care expenses.
If you cannot absorb one month's expenses out of savings or changing your lifestyle to reduce expenses (i.e., selling things or getting a roommate), and you need that next paycheck to cover those necessities even in part, then you're living paycheck to paycheck.
I would also argue that some lifestyle changes are unreasonable to consider... a family of 4 can't get a random roommate, whereas the single millennial in DC/NYC/SF probably should.
I mean, I'm not trying to overcomplicate it... it really is self-explanatory, I think.