In the US the usual phrase is "fish stories," but, yes, in the sentence you've shown us, I would be 99% sure "fish tales" means the same thing. It comes from the idea that fisherman always exaggerate the size of their fish, especially "the one that got away" (so the story can't be verified). There could _possibly_ also be a pun here on the two words "tale" (story) and "tail" (the back end of a fish). The two words are pronounced exactly the same. I DON'T think this is the case here, but it's a common pun. In "Alice's Adventures in Wonderland," for example, we read: "Mine is a long and a sad tale!" said the Mouse, turning to Alice, and sighing. "It IS a long tail, certainly," said Alice, looking down with wonder at the Mouse's tail, but why do you call it sad?" She then imagines the mouse's tale as being a poem, which is printed on the page in such a way that the words actually form the outline of a mouse's tail.

There may be a regional element to this. I have never heard of fish stories, only fish or fishy tales. In the UK anything 'fishy' is either too good to be true, or not entirely truthful.

from the traditional exaggeration by fishermen of the size of fish almost caught

Tale and story are usually synonym. Tales are normally used for unaccurate and sometimes over exaggerating information or untrue report for certain events. Stories can be fictional too but for a newspaper reporter, they take stories as news. And maybe use for something much serious than tale. I'm not an expert but this is what I think. But why fish?