I think (or hope) that what she meant was that if the box went a faster service it would be handled less or at least by less people. The post office nor the UPS nor fed-X have special people for special boxes. The trucks have no air conditioning, they have no heat in the back and very little in the front by the driver. So if its hot out your box will be hot.....um so will the driver. Boxes do get dropped or caught in the conveyors or in "log jams". But for the most part it is an accident, doesnt mean the driver or employee doesnt care about his job.
Most employees dont even notice the notes on the boxes, just look for the sort number or the address label they need to sort the package. Every box has fragile stamped on it, or glass, or liquid etc, what would we do different? like go ahead and drop this one but not that one? Why? makes no sense. At UPS we treat EVERY box the same, makes no difference what is printed on the box. And every box is just as important to the person who is sending it and receiving it as the next persons box. We treat them all the same.
I know a lot of the postal workers in my area and they work the same way at the post office. Seriously they work so fast, really do you think they have the ability to separate and treat differently a box with fragile on it? And do you also treat bags of clothes that say fragile on it or reams of paper that are box printed with fragile on them separately also, and are people willing to pay special rates for special employees?