I'd say it depends on the context. For example, if it's a dialogue tag:
"This is awful," she groaned softly.
...Then I would agree with your editor, as "groaned" becomes the replacement for "said" in this context. If you want to use the other one, then it should be separated from the dialogue with a period:
She let out a soft groan. "This is awful."
(I also swapped the order because it feels more natural to me)
For the most part, though, I'd say it's just a stylistic difference. "A soft groan" feels a little more literary to me.