First off, Miss Fortune's mother was killed by a gunshot wound. Talon does not use guns of any kind. Second of all, Talon is closer in age to Miss Fortune and at that time was living in the sewers of Noxus murdering his companion for botching a robbery, a considerable distance from Bilgewater. Third, Miss Fortune's League Judgment retells her being saved from drowning by a young Gangplank when she walked shell-shocked into the sea after witnessing the murder. She describes him as having the same red eyes and looking almost just like the killer, but younger . Therefore, the elder Gangplank is responsible.
Bonus: Miss Fortune developed a hatred of pirates after the death of her mother. Talon does not in any shape or form fit the description of a Bilgewater pirate. Her beef is not with city sewer slicking street rats.