I'm going to go out on a limb and say that in my experience, parents are NOT the best source of editing or proofing a student's essay. Most parents don't really know what the admissions office is looking for, and many parents are sufficiently removed from writing that their proofing/editing skills are not helpful.
I think in today's world it's probably unbelievable to an admissions official that someone--parent, English teacher, essay coach, college counselor --DID NOT read and help "proof" the student's essay. That DOES NOT mean that anyone should write it for you, or dictate it to you while you copy it down word for word and say you wrote it.
It simply means that most students today are having some adult help proof itheir essay.
Having said that, I would believe that the admissions professional may find your essay refreshingly imperfect and forgive the the occasional spelling or grammar gaffe, if the essay is highly unique, insightful or humorous, or just demonstrates great writing and self perception,
The reason independent college counselors or essay coaches--and this is a generality--
could be more helpful is that often (not always) they spend more time and effort up front on COACHING the essay for topic, originality, creativity and HOW to approach writing. What many parents (who may love you, but often just are NOT good writers themselves) or an overworked guidance counselor does is to take a trite, or unoriginal or hackneyed essay and dwell on punctuation and spelling. It's like going to the junk yard and waxing a rustly heap.