I think the single quotes are correct, and are whats in my history. I think they're arguments to the zmv program, which itself does the expansion and $1 substitutions. Otherwise I think that $1 would be substituted once when you run it instead of for each file.
I've used zmv to also reorganize the directory structure of files too, something that seems easier to do with its glob/variable replace syntax.
Nice to have a cross platform option for usage in scripts though.