The theory is the vinegar rinse will get all the soap out of the coat and restore the ph balance (softness/shiny) to the coat. You must have missed the portions - you only use 2-3 tablespoons of white vinegar in a gallon of warm water to rinse.
So its diluted enough that there is no vinegar smell (or barely) and Charlie didn't have a problem with it. That was my concern at first (the smell).
I washed him with the normal shampoo, then rinsed that all out. As the water was draining, I took the cup and started pouring the vinegar rinse from neck down and on the chest/belly as best I could. I used a large pot (that will hold a gallon of water) to dip the cup in and rinse.
Do not wash that off - just wring the excess water out of the coat and dry them with the towel - then air dry in a room with no drafts.
The only thing I did notice was a small amount of static yesterday after totally dry, but today his coat seems fine. Also it seemed the vinegar tends to make them shed a little more (or its going into shedding season now).
But no vingegar smell
BTW if you want to know how many cups make a gallon - its 16 cups
I had to measure out the warm water in the large kettle