She was right. I mostly roast potatoes with some olive oil dribblings - and leave the skin (scrubbed somewhat) on. When mashing, which I don't do often, I peel but still leave some bits of skin on. I pretty much love all mashed potatoes, but my own are slightly lumpy on purpose.
On the citrus peeling, I do make candied citrus peel, and most recipes warn against having the pith as part of it - there's a strong sort of bitter taste. Me I leave some, not much, but some, don't mind that. But some recipes include it, different tastes for different cooks. So to include the pith, an ordinary sharp knife will do - to exclude it completely, the zester featured above is the right tool.