Does crude oil or kerogen contain ancient DNA?
According to Live Science, the temperatures are in the 120 to 300 degree-Fahrenheit range (48-148 degree-Celcius) when crude oil is forming. DNA in "dry" conditions completely degrades at temperatures above 190 degree-Celcius. Which means that there could be DNA in the oil itself if there are some surviving cells, however, outside the cells there are DNases which will chew up DNA. 

So the DNA they are talking about is like the DNA studied by Gong et. al, where they're looking at the live bacteria in the crude oil, which would be descendants of the bacteria that was around when the oil first began its degradation from organic material.

On both NCBI and PLOS ONE there appear to be a number of papers studying the bacterial growth in crude oil. Which would be why you may have seen articles about DNA in the oil.