I've seen a lot of YouTuber personalities claim that "this is not a paid endorsement", and I'm wondering if this is just legal phrasing that's akin to answering "Have you ever been convicted of a crime?" with "No." when you know you've been "adjudicated" and know the difference. That is to say, can someone promote a product and claim "this is not a paid endorsement" and still receive an exchange from the product owner? Or maybe lying just isn't illegal, so who cares no one will find out. You know, like "I'm not lying because 'paid endorsement' means 'x', and in fact I'm doing 'y'" where 'y' is still an exchange.
Lying is not generally illegal, but deceptive advertising is. The exact extent depends on jurisdiction. In Washington, RCW 9.04.010 states
Any person...who, with intent to sell ...merchandise...place[s] before the public ... an advertisement ... which ... contains any[thing] which is untrue, deceptive or misleading, shall be guilty of a misdemeanor.
"Private meanings" have no legal status, e.g. if someone says "by paid I meant...". If someone gains something of value in exchange for a service or thing, they were paid. However, if one is given a thing for free (i.e. the thing was unconditionally given, without a suggestion that a positive review is expected in exchange), and one then voluntarily endorses the thing (typically because you really like it), that is not deceptive. It is also not deceptive in the relevant legal sense for a business to distribute a thousand samples of the thing in the hopes of getting 6 free endorsements (a pretty low rate).