We have berber up north that we cleaned by hand because the Bissell wouldn't work on it. Spots came back --no shoes in house/ living room. Finally had pro cleaner come in --made sure it was very dry. Most used areas --which is why we needed cleaning --dark areas came back before long. DH says it is from the underpad but how can you prove this anyway ?????
It is a huge room so don't want to change carpet as I would get flooring instead. Would be cold on a cement floor on lower level and I don't want anything that looks like a wood flooring. I know --I will get area rug with flooring for a warmer look.
Think I may try the vinegar/baking soda method when I get home in spring.

If you can make a foam of Tide detergent and hand brush it on, it should remove the stain and not leave the oil base that most carpet cleaners have. Brush it in lightly, let it dry completely and vacuum away