When I was a kid my granddad would pay us cousins to catch him a basket full of grasshoppers and head fish them live on a fly rod in the Brazos River. I don't know if that's true fly fishing but is sure brought home a mess of fish for a family fish fry and it sure was a "natural" presentation!

Natural bait attached to a fly is not considered fly fishing. But, it will greatly increase your catch rate.

I use a fly rod without a reel (Plnor fishing). Although the entire setup is exactly like fly fishing, it does not qualify since I don’t use a reel.

Hemingway fished fly rod set ups rigged with worms or bait, so did many others back then. Fish how you enjoy fishing.

Flies are simply little lures delivered with fly tackle. Bait in is totally fun too.

As a kid in Jersey I recall a couple of opening days for trout. Guys with fly rods would crowd the pools, which were invariably high and muddy from spring rains. And most of those fly rods had a salmon egg on the hook. Occasionally someone would use worms. But never flies.

I have caught catfish on a fly rod using orange scuds.

I fish for records and although you can tip a fly with bait, that eliminates the chance at a fly fishing record. You can still get a rod and reel record using a fly rod with a fly tipped with bait.

The TPWD states for fly fishing:

The lure must be a recognized type of artificial fly. The use of any other type of lure or natural bait, either singularly or attached to the fly, is prohibited.

I really enjoy reeling in a fish on a fly rod and there are times I have added a bait to my fly.