Few TV shows are as iconic or as genre-defining as Friends. It tells the story of six friends in New York- that's the entire premise. The rest of the story is built around the personalities of the characters, which leaves the show open to be either fantastic or terrible. I believe that despite some shortcomings, Friends is a true story due to its openness, honesty and its surprisingly realistic characters.
One of the reasons I think Friends is a true story is because it doesn't claim a deeper meaning. Nothing “happens for a reason”, it just happens. Within that framework, the characters and story explore a peculiar type of honesty. All of the characters are inherently flawed, to the point where sometimes they're just downright unlikable. This makes them feel more like "real" people, even when they act completely unrealistically.
It's not perfect, of course. There are several issues with Friends. For example, the "everything works out in the end" trope and the almost-too-perfect romantic pairings between the characters by the end of the series. This, however, is a conceit of the genre in my opinion. The situations and reactions may not be the most realistic, but a truly realistic sitcom would be incredibly boring. Once you suspend disbelief, Friends delivers on exactly what its title promises, and in the process becomes a very true story about people just living their lives.