My son is also in the 3rd grade. As in your household, he also does his homework at the kitchen table while dinner is being prepared, and I do EXACTLY the same thing you do. I do not give him answers, but I am on hand to answer questions and to reinforce what has been explained in the classroom. I do point out if something doesn't look quite right, and I ask him to check it and correct it (if need be). I, too, point out the importance of him taking pride in his work and being sure it is done neatly; not always as neat as I would like, but if the work is correct, I do let that go sometimes, mostly because my son is not focusing any longer because in his mind he has finished, and it looks ok to him. He's actually right, he has finished, and I have to keep myself in check that it doesn't have to be perfect, and it is ok for him to get some things wrong. It's a learning process for all of us!
I have volunteered in the classroom, and the teachers LOVE it when the parents reinforce what has been taught. They love it when the parents ARE involved in the homework process; it shows the kids that homework is important and that their parents care. It shows the teachers that the parents care. You can definitely tell when a parent has not checked over the homework or when a parent is not involved in the process, and it is the child that suffers.
Don't get me wrong, I think the level of parental involvement that is expected nowadays is a little overboard, and it is an extremely frustrating process in our house at times; both for me and for my son. I also feel that the volume of homework my son brought home every night in the 2nd grade was overboard. It was actually more than a friend's 5th grader had each night.
Having said all of that, I have noticed (finally) some positive response from my son with regard to homework and the neatness, etc...
Now, when he gets older, I probably will not be as hands-on with homework, but right now, they ARE still little/young! I don't recall ever having homework in these very early school years. Times have changed, and I am trying, as are you, to raise a scholastically successful kid. If it feels right for you, keep doing what you are doing - don't bail on your son because a co-worker would do it differently.
Sorry for the wordiness...homework is a subject that comes up a lot in my neck of the woods. Hope this helps you. :-)
KimD