Yup.
One time I decided "to be healthy" and bought a jar of organic pasta sauce, low calories, no preservatives.  I'm just one person, so I used some and put the rest in the fridge.  No joke it was green in a week.  I dont even know which day it turned bad as I noticed it one day so maybe on day 4 or 5 it started already turning bad.
So for anyone buying that sauce you got to basically use it all in one shot or maybe over a few days tops.  Absurd.