Recently, I read The Subversive Copy Editor by Carol Fisher Saller. Saller is a copyeditor at the University of Chicago Press, home of the celebrated stylebook, now in its seventeenth edition. She also manages the question and answer feature on the stylebook’s website, which has been a huge resource to me over the years. I’ve followed happenings at the University of Chicago for quite some time — since the fourteenth edition!
I wholeheartedly agree with Saller’s take on copyediting and the Chicago philosophy in general. One of the sentences in the opening pages of the book sums it up perfectly:
Your first goal isn’t to slash and burn your way through [the manuscript] in an effort to make it conform to a list of style rules. (p. 7)
Unless you want someone to change your work radically (which I would suggest is substantive editing, not copyediting), this lighter and sensible approach to copyediting should put you at ease. When you hand over a manuscript for copyediting, you feel the work is in pretty good shape and that it needs some fact-checking and smoothing (and, in many cases, formatting help for references and bibliographies).
So remember that unless you are submitting an article for a publication with strict guidelines or your work needs a lot of retooling, the copyediting process should be pretty gentle.