While this common claim isn't true, it is also not totally false, and the claim exists for some good reasons. So what's actually true?
In three studies we analyzed (where people had been asked what their ideal number of hours of sleep they need to feel their best), the average responses were 7.5, 7.7 and 7.7 hours. And 8 was the most common answer. These numbers come very close to matching the often cited figure that, on average, sleep cycles are 90 minutes long, and people have 5 of them on a typical night, leading to 90 minutes * 5 cycles = 7.5 hours of sleep.
However, in all three studies, at least half as many people chose 7 hours per night as chose 8 per night, with 9 hours or 6 hours being the third most popular choices. In fact, in each of the three studies, more people chose a time other than 8 hours than chose 8 hours.
The reality is that different people have different sleep needs. It's generally believed that genetics influence how much sleep we need - some lucky people need less. Environmental factors (like chronic health issues - which can impact sleep quality) and age also play a role. And the heuristic that people sleep for 5 cycles of 90 minutes each is also just an approximation - in practice, the duration of sleep cycles varies.
To give a specific genetic example, some research suggests that a mutation in the DEC2 gene in both mice and humans may impact both sleep duration and speed of recovery from sleep deprivation.
One doctor acquaintance of mine, I kid you not, only needs 5 hours of sleep per night (true for all of his adulthood, with no seeming impairment). He told me he was trying to figure out how to sleep more since it's annoying being awake so much earlier than his wife.