If you put citric acid into water in a jar, it will dissolve. If you pour oil onto that water, it will float as a separate layer. Presumably, if you shake the jar, the solution will emulsify and will then split. I haven't done it, but a salad dressing is basically an acid and an oil and it will split. If you add detergent to the jar and shake, it will foam up and form a single stable solution. Something in the detergent allows the oil to 'dissolve' into water. (From memory, surfactant molecules form a micelle around the oil, but I know that there are other things in the detergent as well.)
If you take a pan, put some vegetable oil in it, add ground coffee and apply some heat, it eventually starts to smell like a dirty group head (yes, I have done it). If you do a few clean water backflushes and remove the shower screen from your machine, you will probably still be able to wipe something off it.
I think that it's a fair bet that some of the stuff responsible for dirty group heads is not water soluble (hydrophobic); probably coffee oils. How is backflushing with citric acid going to remove those compounds? Wouldn't you need a detergent to do that?