The only reason I see for turning the bag inside out on the trail is to air it out which I generally do immediately after I get up while I get some breakfast.  I can't see how it would help with packing except that if you do turn it inside out in the morning to dry out then it saves some morning time if you pack it that way.  You still have to turn it right way out the following evening so there is no net time saved.  I woudn't do that because if any water gets through to the bag during the day or if it is raining when I set up I want the wet on the outside of the bag.  Some sleeping bags do have different material on the inside but from what I have seen the outside material is more slick.

Storing is a different matter but again it is about airing out the bag not ease of packing. really I have no idea where that "helpful advice" is coming from and I would ignore it.

Although it does occur to me that the inside of the bag is smaller than the outside so technically there is less exposed surface area if you turn the bag inside out and  theoretically that could result in less stuffing effort...but probably only if you  discount the effort you spent turning the bag inside out.  Possibly with overstuffed  or very puffy bags it makes a difference.