Not true. Many true araucana breeders use tailed birds in their breeding pens. Ditto for birds without tufts. The birds exhibited, however should be rumpless and tufted; otherwise they will be DQed.
The silkie gene is recessive. A bird has to have two copies for the trait to show. All chickens with silkie feathers have two copies of h. Yes, it could be a random mutation, aka sport, but that would be fairly uncommon. A recessive gene can lurk and hide for generations.
There are quite...
Looks to be a silkieXaraucana; one variation of an Easter Egger. Very pretty colouring. She has more than one generation of silkie in her to have acquired silkie feathers.
If she lays a blue egg you could try breeding the trait into a line of grey or partridge silkies. She looks to be grey...