I agree with both of these. The Emily Post method is what I was always taught growing up; I’ve seldom been able to make myself do it.
It works with things like fish bones, where you can clean them off with your tongue and return something fairly non-offensive to your plate. But a bite of chewed-up gristle? It’s the napkin for me.
A lot of etiquette rules center around not ruining your hostess’s beautiful hand-wrought table linens. This does not apply in steakhouses. But if you are in a private home and they appear to be hand embroidered or crocheted with lace at the edges, that is the time to use your fork and cover the spot on the plate with some parsley.
Another thing to remember, if you are forced to do so and have to sit there with this yuck on your plate: it’s not your faux pas, it is that of the chef. Just as when one is forced to use a knife to cut the salad into smaller pieces. It’s not rude to cut your salad; it’s rude to serve a salad in pieces too large to eat in a single bite.
I do still think asparagus should be picked up with the finger tips, but follow the lead of your hostess in all things.