The main problem with oil and grease after allowed to sit on concrete for extended period of time is that the oils penetrate the concrete, since concrete is a porous material. I have witnessed concrete slabs after demolition at a former gas station. The oil had penetrated the concrete 3" plus. This is why in many cases a "shadow" remains.
One recent example: As many of you know Toyota has had it's share of recall issues recently. I have performed dozens of oil spill projects for Toyota since the first of the year. On several Toyota models, an oil line failure is apparently an ongoing issue.
The first call for service I received was for 2 separate locations in Sun City west. The responsible dealership first tried to resolve the issue themselves. They sent an employee our from their service department. His first step was to apply oil dry on the oil spills (exactly what needs to be done immediately to absorb the surface oils). His next steps resulted in disaster. He "assumed" that pouring brake fluid and paint thinner on the oil stains, followed by using the portable, cold water pressure washer he brought with him would be the answer.
The end result was the oil was diluted and actually forced deeper into the concrete by his decision to use brake fluid and paint thinner. Then the diluted oil was most likely forced deeper into the concrete when he used the cold water pressure washer (with a zero degree tip, I forgot to add, which left it's own damage to the concrete).
As I mentioned, there were 2 separate properties involved by this 1 oil line rupture. The owner of the Toyota didn't realize the oil when he left his residence and drove over to his girlfriends residence, spilling oil all over her driveway also.
End result; 2 driveways that could of been resolved properly for a few hundred dollars. Learned from the region manager of Toyota that is my main contact now that these 2 properties required a concrete coating contractor to remove the sections where the oil was forced deep into the concrete, patch those areas, then perform a complete overlay of both driveways. Did not share the exact amount spent, but he did tell me it was in the thousands of dollars.