Is it Olefin carpet?  If it is and it has been flushed 6 or 7 times (even though it was Stanley Steemer) they may be permanent.  Olefin carpet is like an oil sponge.

Try rubbing your hand on the spot for a few seconds.  Is your hand oily?  Try a terry towel does it get oily?  If not then it may be a stain that will never come out.

If they are oily you need to attract oil more then the olefin to get it out.

If you were a HWE guy I'd say a really high pH pre-spray like Flex from Bridgepoint, mixed with Boost All and Citrus Solv, with as high heat as you can get.  After cleaning coat the area with Stain Absorb.  Return the next day and vac and check results.

If you do not have HWE then I'd try the 50/50 mixture of Encap-DS for spills and stains with some FP Max pads on your Cimex.  (If you don't know what the 50/50 mixtuure process is do a search on this board for it).  Return the next day and vac and check results.  You may have to repeat several times if you see results.  I'd post bonnet with terry cloth too when I think I am done, to finish off, dry and see if you get oil transfer.

But either of these methods will only work, if the oil is not set into the fiber.  You need to Pre-Qualify that with your client before doing any work.  Sounds like Stanley Steemer did not do that with them.