It is not that Trump would likely lie about it, but anyone looking at him will notice something not quite right. This is the impact that a rug has on everyone.
Toupees have improved over the years to a degree they look like and often are real hair. The problem is, no matter how genuine the hair looks, it does not look like the hair that belongs on the head of the person that wears it.
Trump’s toupee also has a significant flair to it . For any man to have such a hairstyle, which none his age do, it implies he has a hairdo every day, but one merely notices the other aspect of a rug. It is always the same, every hair in the exact same location, and the length never changes. Even the wind does not move the hair into the eyes, because it is essentially glued in place.
A rug has an heir of dishonesty to it. An obvious rug tends to make people uneasy. While it may not appeal to women, if Trump shaved his head, we would be more at ease.