Whose label says it's fake? The VAM Book can be used to identify altered coins if you can show that one of the dies was used on a die pair from a different mint. An example I've seen is an altered 1889-CC "sandwich" coin made from an 1889 obverse (you could tell by the strike it was a Philadelphia obverse) and an 1884-CC reverse. It can also cast suspicion if there's no match in the listings for some attribute of your coin. In the case of your coin, the high S mint mark with normal date isn't a known combination. I would suspect the S could be added. Look for signs of it being glued on or retooling on the nearest reeds from an embossed mint mark. The lines in the cotton blossoms aren't really a red flag, since that's a common place for those to show up. "In God we trust" looks fine. The die crack doesn't ring a bell, but it could very well be something on a known 1896-P. 1896-S typically has a needle-sharp strike, too, but mint records show there are dies that were used for over 500,000 coins, so there should be some that show die wear, as well.