Absolutely nothing in this movie could've happened (spoilers)

Vertigo may have been beautifully shot, but it had one of the most inane scripts of all time.

Let's take the famous tower scene when the suicide is faked. When "Madeleine" commits suicide, Scotty would have definitely seen the body right afterward or seen photographs of the real wife in an obit or newspaper headlines somewhere. There's no way that at some point, he wouldn't have come across something that informed him that there were actually two women.