"I leaked nothing to nobody." - SAE? AAVE? Deliberate double negative?
Solution 1:
It's not a dialect thing, it is grammatical standard English.
The "double negative" rule applies to situations where you have two possible negation strategies, one being a negated auxiliary verb + a negative polarity item; the second being a content word with negative meaning.
(1) I have not leaked anything. [Negated auxiliary + NPI (anything)]
(2) I have leaked nothing. [Content word with negative meaning (nothing)]
The rule is that you can't use both strategies at the same time. Also, related is that using an NPI like anything or at all can't be used with a non-negated main verb:
*I have not leaked nothing.
*I have leaked anything.
Rice uses strategy (2), instead of strategy (1) (which would have been I didn't leak anything to anybody.). This is a more direct way of speaking and is well suited to the spoken medium.
Solution 2:
"I leaked nothing to nobody" is not considered standard English, as far as I can tell. It is possible to use multiple negative words in a single sentence wtihout them cancelling out in some circumstances, but I don't think this is one of them. (A random example I can think of that would be standard is "I wouldn't sell the farm, not to him.")
- Non-Standard Dialect: He didn't give nothing to nobody.
- Standard: He didn't give anything to anybody.
(I-Language: An Introduction to Linguistics as Cognitive Science, by Daniela Isac & Charles Reiss)
"I leaked nothing to anybody" is perhaps "technically" correct, but it sounds unusual to me; certainly less natural than "I didn't leak anything to anybody."
It often sounds more natural for negation to be marked "at the sentence level" (by a negative auxiliary like "didn't," or an auxiliary accompanied by the negative particle "not") than with another specific negative word. This applies equally as far as I know to dialects with negative concord: the Yale Grammatical Diversity project overview of this phenomenon only covers cases where specialized negative words occur alongside sentential negation, not in place of it. It is only a short summary, however, and it does point to a further source you may wish to consult:
There is variation in the types of negative concord that different English varieties allow. For an overview, see Smith (2001).
Clause-level or verbal negation is also the most usual/"expected" state of affairs from a typological standpoint ("On the typology of negative concord," Johan van der Auwera & Lauren Van Alsenoy); that is, sentences structured like "John bought nothing" (taken from van der Auwera and Van Alsenoy) are uncommon worldwide. So I find sentences like the one you quote here, where clause-level negation is not used but multiple other negative words are used, to be interesting and somewhat surprising.
I did find other examples of this type of negative concord, if that's what it is (multiple negative words but no clause-level marker of negation), on Google Books:
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I never says nothing to nobody (The Melodist, Vol. I, by H. Arliss)
(this one also has the negative word "never," which may be relevant)
Here is me nabs saying nothing to nobody but working away at a pome in his head with a pick in the hand and the sweat pouring down off his face from the force of his work and his bloody exertions. (The Various Lives of Keats and Chapman: Including The Brother, by Flann O'Brien)
[...] my name is nothing to nobody. (Retrospections, Social and Archaeological,* by Charles Roach Smith)
Dat other black boy was hoeing cotton way in de back of de field and de patroller rid up and down de big road, saying nothing to nobody. (When I Was a Slave: Memoirs from the Slave Narrative Collection, edited by Norman R. Yetman)
If you try to be all things to all people, you will be nothing to nobody. Selling to the Top: David Peoples' Executive Selling Skills, by David A. Peoples
You can see that the examples seem to come from a diverse group of speakers. Negative concord is a feature of AAVE, but it is not at all a distinctive feature; it's widespread in all sorts of varieties of English, particularly colloquial speech.
I don't find it at all plausible that the statement was intended as "weasel wording" or "litotes."
Note that people speaking spontaneously often don't produce grammatically correct, complete English sentences. False starts, self-interruptions and tangents are the norm. I find Andrew Brēza's suggestion ("Listening to the audio recording of the statement makes it sound like she was abbreviating these two thoughts into one sentence: "I leaked nothing. I leaked to nobody." If she were writing her remarks as part of a speech I'm sure she would have worded it differently.") very plausible.
Edit: I just noticed there is a Language Log post on the topic by Mark Liberman. He refers to it as "emphatic multiple negation." I would recommmend reading it and the comments below.
Unfortunately, I don't have access at the moment to a grammar that explains whether this exact use of negative words with each other is standard or non-standard. (The Isac and Reiss quote at the top of my post uses an example with a negative auxiliary "didn't".) However, here are some Google Books snippets that I found that I think back up my feeling that sentences with two specific negative words ("n-words") and no clausal negation like "Nobody did nothing" are cases of negative concord and not generally considered standard:
As Alison Henry points out, they are Positive Polarity Items in the strong sense that even in Negative Concord dialects, which allow, for instance Nobody did nothing as synonymous with Nobody did anything, the examples in (5) remain ... (Syntax at Santa Cruz, Volumes 1-3)
Juan never to nobody did nothing. Juan never did anything to anybody. The traditional grammars claim that the Negative words before and after the verb have to be different. Because this seems too obvious, it is better to claim that... (Chicago Linguistic Society. Regional Meeting - 1991)
For example: Nobody did nothing means everybody did something. The correct negative sentence is NObOdy did anything. (Test Your Grammar, Rachel Bladon)