An appeal that only says "this person was never our customer" asks Google to enforce a rule it doesn't have. The appeal has to show the review isn't based on the writer's own experience. Under Off-topic, that comes from the review's own words, not from your records.
Your search is still worth doing, for your own sake. It can miss real people, though. Google shows whatever display name the reviewer picked, and it doesn't have to match anything on an invoice. The job might sit under a spouse's name, a parent's, an employer's, or a nickname. So search every version of the name you can think of before you call the result empty.
Done that way, an empty result tells you the review probably means what it says. The appeal doesn't lean on it. It leans on the review's words, like Kevin's "I've never called them or used them," and on what actually happened, written down with the date.