I think the reason some people might believe this claim is because we’re taught in school that the moon’s gravity causes the tides. I think the reasoning goes, “well if the moon’s gravity can affect the tides, surely it can affect smaller things too”
The moon actually pulls on the land a little bit but it’s such a small amount it’s only measurable with very specific instruments and in large timetables. Not enough to really affect any individual on the planet.