You're not kidding.
I'd like to delve deeper into the "Jumpman is Mario's Father" angle.
These are the requirements for the theory to work: "Lady" is a different character from "Pauline", "Donkey Kong" in the arcade is a different character from "Donkey Kong" in the Country series, "Donkey Kong" the arcade game is a different game to "Donkey Kong" the Gameboy game.
None of these are unworkable, so let's go.
- Making Donkey Kong (Arcade) the chronologically first game in the series has that lovely "the start of everything" charm to it.
- Jumpman being Mario's father explains the difference in personality needed for Mario to do what he did to DK in the Donkey Kong Arcade backstory and Donkey Kong Jr.; say what you will, but Mario does have a personality, and "abuses animals" isn't considered part of it (except in terms of player action).
- Jumpman can be the family name of the Mario family ("Uh, it's pronounced 'Jumpmun'.")
- "Lady" could be Mario's mother. Lady was kidnapped in Donkey Kong (Arcade) and history repeats in Donkey Kong '94, where the DKC DK kidnaps Pauline (Mario's girlfriend). Why? DK kidnapped Pauline in the Mario & Donkey Kong series over toys, so who even knows what his motivation was.
- With Jumpman being an older person than Mario, Rare's canon that "Cranky Kong is DK's grandfather and the arcade DK Jr. is DK's father" makes total sense (as for who the Gameboy DK Jr. is... ¯\_(ツ)_/¯).