The Gruesome Backstory:
You have Russian mystic Grigori Rasputin to thank for those disclaimers. Well, not directly, seeing as how he was utterly, thoroughly, painstakingly dead by the time MGM released their 1932 film Rasputin And The Empress. Rather, the impetus came from Rasputin's head murderer, Prince Felix Yusupov. In the film, Rasputin is murdered by Prince Paul Chegodieff, but not before the mystic hypnotizes and rapes Chegodieff's wife, Natasha. Now, Prince Yusupov had been in no way secretive about his role in Rasputin's murder, so he reasonably posited that audiences would equate Prince Chegodieff with him, and by extension assume that Rasputin had his mystical dong all up in Yusupov's wife, Irina -- whom Rasputin had never even met.
"His dying words were, 'I never fucked your wife, and while I have length, yours is clearly the more girthy and powerful dong.'"
The Yusupovs sued for defamation, and a jury agreed with their claim, awarding them $125,000 in today's money. If that seems somewhat paltry, we should note that the total court costs for MGM nearly equaled the film's entire production cost. As a direct result of the case, MGM and other studios began slapping the "Any Resemblance To Persons Living Or Dead" disclaimer on every last film they produced -- even those clearly based on actual persons living or dead.