Who's the Cousin? Cousin to Whom?

My mother's father, Willard S Parker, had an older half-sister, Dora (m Potrafke. She was the daughter of John Arthur Parker (b Danville, Des Moines County Iowa 1879) and Essa Swing (b Clermont County, Oh 1881.) Dora was born in July of 1900.

Dora's half-siblings

In 1905, John Arthur married again, to Maggie Purkiser, and they had three (known) children: Estel, Willard, and Gladys.

In the meantime, Dora, family lore says, was living with/being raised by "cousins." We have been trying to figure out exactly who the cousin is and how they are related.

The 1910 Census has Dora in Williamsburg, Ohio, in the household of Frances Vanosdol, who was sister to Dora's grandmother. However, this Frances has no listed relationship with the Head of the Household, one James Burnett. Mr. Burnett is credited with being married to a Mamie nee Fitzwater, and they have a daughter Ella.

The Burnetts, while claiming no relationship with Frances, who is Aunt Dora's aunt, do claim Dora as a "cousin."

So -- who are these people? 
How are they related?

There is a Burnett married into another branch of Parkers. (We already have two of those lines fairly well proven. Just what we need, a third Parker branch!)
There is a Bennett married in with the Vanosdols, mother of Sarah Ellen, who married the Mystery Laycock.
There are a few Barneses scattered into the lines, here and there. 
All of these are possible variations of the name for a census taken orally, and by and from people who may have been illiterate or have unfamiliar accents.

It's more a curiosity than anything else. Family lore vs Family Facts. How is this Unknown Man claiming cousinship with our aunt, but he is no kin to a woman who is her kin?

Just another historical mystery, shrouded by time and fuzzy connections.