There's a serious customer relations problem here in how they bill this. When they do it this way they make themselves look as if they're very nearly giving you the small part for free, it's the shipping they're really making their money on.
Sometimes perception is the problem.
So when you point out that customer always pays, yes, I agree. The problem now is how this is presented. The manner of it's billing and the hard ass attitude of "take or leave it" kills customer loyalty.
My own personal experiences over the past 50 years leave me with a mental list of places I just won't do business with. Yet there are others that do the right thing (however that's defined) and get my business over and over. Those people are the ones that don't leave me with a feeling that I've been screwed as I walk out the door or confirm my online deal.
So in the end, in addition to good business sense, it'd pay to also have good people skills.