The Dursleys:

[hickengruendler]

No: HPFGUIDX 167552

 
> 
> JW retrieves a few JKR quotes:
> 
> "Everyone who shows magical ability before their eleventh birthday
> will automatically gain a place at Hogwarts; there is no question of
> not being `magical enough'; you are either magical or you are not.
> There is no obligation to take up the place, however; a family might
> not want their child to attend Hogwarts."
> 
> We are not told what happens to a no-show.  Would a headmaster allow
> a muggle-born 11-year-old be a no-show without consulting the muggle
> parents? What would Hogwarts do with a no-show who later wanted to
> start training?  Is such a person left with Quickspells mail
> correspondence courses as the only alternative?
> 
> "Aunt Petunia has never performed magic, nor will she ever be able 
to
> do so."
> 
> It appears that most magical kiddies generate untrained,
> uncontrolled, spontaneous magic (i.e., the vanishing glass that 
freed
> the snake in SS/PS). A literal interpretation (always dangerous!) of
> the quote means that this NEVER happened to Pet.  However, I find
> nothing on JKR's site that calls Pet a muggle.  Have I overlooked 
the
> quote, or is it in an interview, and not shown on the JKR site?
>

Hickengruendler:

"Is Aunt Petunia a Squib?

Good question. No, she is not, but—[Laughter]. No, she is not a 
Squib. She is a Muggle, but—[Laughter]. You will have to read the 
other books. You might have got the impression that there is a little 
bit more to Aunt Petunia than meets the eye, and you will find out 
what it is. She is not a squib, although that is a very good guess. 
Oh, I am giving a lot away here. I am being shockingly indiscreet."

>From here: http://www.jkrowling.com/textonly/en/news_view.cfm?id=80

IMO, these answers are pretty clear. Aunt Petunia is a muggle, who 
has never done any magic and never will. Granted, JKR is very tricky 
sometimes (see her answer to the question, if we'll here about 
Regulus), therefore I would be very careful about everything she 
said, but I really don't know, how she could sneak out of this one.