I am always a supporter of "restoration" instead or "refinishing" If you strip a finish and apply a new finish etc it looks like a new table and ruins the wood's natural patina. This is what they mean by discouraging refinishing. My suggestion would to research furniture restoration techniques to determine what your problem may be. It is probably a wax finish. There are many articles on repairing water damage on wax finishes. You could also search for "furniture restoration or repair" in your area to consult a professional.

OK, now we've got some questions answered. You're table is oak,not walnut. It is solid, it would have been very unlikely that it was walnut and solid ( also would have been odd that it was so new and walnut). My only concern is that you have to realize that trying to make oak look like walnut will be difficult. I'm not sure how handy you are,refinishing anything even a flat surface like this table is not as easy as it looks. As far as stain selection goes, once you've stripped and sanded the entire table , use a leaf as your color sample and try diffrent stains on the leaf ( just a small section , make little "swatches" ). After you get the color you want, use some mineral spirits to clean off those stain samples , sand the leaf again and proceed with your staining.

I am not an expert by any means but I have painted a lot of furniture in my house. I would prob lightly sand the chipping areas. I have limited use of chalk paint. I did chalk paint a few chairs and my dining room table. My tabletop was very shiny so I lightly sanded it and then I primed it. I used the chalk paint on top of the primer and then a coat of poly. It has held up fine for over 4 years now. When I paint I usually use just regular off the shelf paint from Lowes or Home Depot. I just painted my entire bedroom set. I did no sanding at all. Just a good primer, painted with Behr regular paint and again a coat of poly on top. Hope it turns out well!

The following is my opinion. Seems like a lot of work to get it the way you want it. I'd sell/donate it and get what you really want. You can paint a pig, but it's still a pig.