Hi Victor, you are correct, but the main essence of the joke is the claim that it's true, the fascinating thing is the U.S. Navy used to actually have a website designed solely to deny it was true. The irony is, it is the strength of the US Navy's denials that led so many to come to the belief it might actually be true.

Whether it is not, who knows, and I suspect it actually comes from a joke dating back to the 1930s. There is a variation using a British ship, which would make sense if the joke had originated from the 1930s.

But who knows, and the crazy thing is, this joke has such legendary urban myth status, that it even has a Wikipedia page talking about it, the craziest thing of all, it's impossible to disprove it which is why, even with its implausibility, it sticks around as a potentially true story:

https://en.wikipedia.org/wiki/Lighthouse_and_naval_vessel_urban_legend

Thanks for the comment, Victor!