The good thing about well sourced data across millions of sample points that are prepared by professionals over decades of collection is that one should believe that data over anyone’s uninformed beliefs based on no carefully measured data over even a single person.
That's all well and good, so where's the link to the studies and the studies' parameters? It's not like I'm denying well presented findings. In absence of those, I can hold skepticism about the claims.
My definition of paycheck to paycheck would be that if you lost your source of income you would not be able to afford living (housing, food, healthcare, insurance, etc.) within a certain window of time. The data can be easily manipulated depending on what you consider essential. I would be surprised if findings by the Federal Reserve include healthcare as a necessity or essential. It's easy to say it's not an essential if a family or individual never had it.
Most people are not able to live without a source of income through working. And this _should_ be the norm - most people _should_ be working in their adult lifetime.
It should not be possible to live indefinitely without having to produce output that somebody in society needs (and thus is paying you to do so). The welfare state is to prevent the negative outcomes of someone in destitute, by preventing (or trying to prevent) crime, etc. It isn't there so that one can live free.
It's not a big caveat. How else would you define paycheck to paycheck? I'm talking about days, weeks, or low single digit months. A window of time is not indefinite.
The point of measuring people living from paycheck to paycheck is to measure their ability to have financial security. You are financially unsecure if you cannot pay for essentials for days, weeks, or a month off of savings. Many people in the U.S. are completely unable to save up for more than that. That's literally the point of talking about people living paycheck to paycheck. And usually, people only refer to being able to pay for food and housing. It rarely accounts for saving for retirement, health care, home/renter/car insurance, etc., all things that should be considered essential for living but are typically not in these studies.