"Woody Allen Speaks Out", NYT 2/7/2014:
Not that I doubt Dylan hasn’t come to believe she’s been molested, but if from the age of 7 a vulnerable child is taught by a strong mother to hate her father because he is a monster who abused her, is it so inconceivable that after many years of this indoctrination the image of me Mia wanted to establish had taken root?
As usual, it's hard to keep score, but there might be an extra negative in that first clause.
This seems to be a case where the remnants of negative concord are not quite in balance with the logic of negation cancellation. Here are a few (of the relatively infrequent) web examples where "not doubt that not X" means "concede that X", as in Woody Allen's usage:
In last nights episode, Olivia told Edison that she loved him, and I don’t doubt that she didn’t love him, but the thing that got to me was that she said it so easily. (= "I concede that she loved him")
My dad, being as decent a man as he was, if he said he was going to be somewhere, he was. My mum could be unpredictable. I didn’t doubt that she didn’t love me — I know she did, and I her. But being in show business, dealing with alcoholics (Ted Andrews) and becoming an alcoholic herself, she was not as reliable as was my dad. (= "I concede that she loved me")
I have to say, I didn’t doubt that it wasn’t black. In fact, I don’t think he could get much blacker. It hasn’t really rejuvenated his hair, just covered it in tar. (= "I concede that it was black")
Here are some web examples (apparently much more frequent) where "not doubt that not X" = "concede that not X", the opposite of his usage:
No matter what you say, comparing a bunch of headphones in a retail store does not make you an expert on all the headphones you heard. Sure, you might get an idea on what you liked or did not like, but you will not be better informed than someone who actually owns them and has heard them with different amps and under different conditions. I don't doubt that you didn't like them, or that your impressions do not change over extended periods, but that does not make this a bad headphone. (= "I concede that you didn't like them")
I agree, but it answers those who go the other way, and find Rashi inconclusive. I don't doubt that it isn't unanimous. (= "I concede that it isn't unanimous")
I wrote the ugly code in question. I don't doubt that it isn't particularly performant and honestly I never run any of the throttling code in production. That said the intention was to implement the size calculation in a way that didn't require a lock. (= "I concede that it isn't particularly performant")
It would be very interesting to see what a Russian audience would make of our efforts because I think British choirs make a very beautiful sound, but there's no doubt that we don't make the same kind of heavy and really strong sound that the Russians do. (= "I concede that we don't make the same kind of sound")
They don’t consciously do it, I have no doubt that they don’t realise that they are denying the Saviour, but indeed they are, and in many cases with a vehemence! (= "I concede that they don't realize that they are denying him")
No doubt that guys don't like to use feminine products that smell girlish. But they love to smell these things on their girlfriends. (= "I concede that guys don't like to use feminine products")