This is the natural result of one side having no evidence other than "dude trust me".
Neither side has any evidence.
Harris has asserted without evidence she worked there. Trump has asserted without evidence that she didn't.
And before you go all "HoW cAn He PrOve A NeGaTiVe", if someone who knew her at the time was calling bullshit on her claim, or McDonalds themselves were, then that would be evidence she's lying.
I don't know what evidence you'd expect her to have. Who keeps evidence of a temporary job from 40 years ago? Even McDonalds themselves are saying they don't keep records going back that far. Again, the level of evidence required depends on the claim. Someone saying they did a temp job at college - why does it take some massive leap of faith to believe that? A fairly senior colleague was talking about her CV - giving me some advice on mine - and she said she was told to only put relevant things on it. She said to me "that's why I don't include my year working as a florist". I didn't scream at her "PROVE IT!!!". It's not some outlandish claim.
If you think it is a "nonsensical belief" to find it plausible that Harris had a job in colleague then why do you think that?