Geeky and tacky

Here’s something that just occurred to me. For all I know others have thought of it already.
According to the writers of the episodes she was in, River Song was not a Time Lord.
She was ‘just’ a normal human female born in the TARDIS and suffused with the energies of the ship. (The TARDIS apparantly liked her: they’re both cheerfully amoral.)
But…
If you believe the load of nonsense Chibnall wrote into the last series that doesn’t work. Because only the Gallifreyans who had been genetically altered to include the regenerative ability of the Timeless Child could regenerate.
And that’s not possible unless River was the child of the Doctor and not of Rory.
And that would mean the Doctor marrying his own daughter.
Geeky and tacky at once.
You see what trouble you get into when you don’t care about continuity?