Are you sure this is the same thing? The word ‘petroleum’ is not in the paper you link.
Naively, I would think the paper you linked is about carbon (the charcoaley substance) derived from vegetables being used as a black food coloring, and the poster above is talking about “carbon black oil”, a type of oil derivative that looks black - two completely different things.
> Carbon black (with subtypes acetylene black, channel black, furnace black, lamp black and thermal black) is a material produced by the incomplete combustion of coal tar, vegetable matter, or petroleum products, including fuel oil, fluid catalytic cracking tar, and ethylene cracking in a limited supply of air.
"Carbon black" refers to both types, but "carbon black oil" is referencing the petroleum derived one which is not allowed to be used in foods as far as I know.
It would appear that it's the PAH content of petroleum derived carbon black that is the carcinogenic component
https://www.efsa.europa.eu/en/efsajournal/pub/2592