No, I don't think that's the reason. The moon is frequently very bright during the day, not even remotely hard to see. Moreover, people are mostly outside during the day, meaning that most of the time they have the opportunity to see the moon will be during the day.
I think the reason is that a supposed sun/moon - day/night dichotomy is perpetuated by culture (for instance, clock dials that use an image of the moon to symbolize the night) and that culture has a stronger impact on people's perception of the moon than their personal observations of the sky. I think they have seen the moon during the day, but the moon is very rarely the object of their attention. They see it, but rarely do they notice it.
The reason for such a culture emerging seems obvious to me; the Sun's presence in the sky obviously correlates with daylight perfectly, making the sun an obvious symbol to associate with the day. But then what symbol would you use for the night? There's a clear day/night dichotomy, creating a demand for a symbol that's inverse of the sun. However there's no object in the sky that correlates so perfectly with the night. The moon isn't there half the time, but neither is any particular star. You could use generic stars, and sometimes that's done, but stars aren't necessarily visually distinctive. The moon is visually distinctive and so it's pressed into the roll of being the symbolic opposite of the Sun, even though a trivial glance into the sky reveals that it isn't actually opposite of the sun.