I've just come across a film review by an American author where he says: "I can assure you that both are not typical in any part of this state". In negative sentences like that, my inclination would be to use "neither one of them is..." instead (or, depending, none of them is/are...). Is it right to say "both are not..." ?
Without hearing the full context, there may be a danger of confusion. Both may convey a sense of each as in both dogs are blue or it may convey a sense of a combined entity or occurrence, it's dangerous when it is both raining and snowing.
While the latter meaning is more common when both is a conjunction rather than a determiner or pronoun, that is not always the case. I'll pay you when I get both.
When there is a negative in the sentence, it may be more difficult to determine which of the meanings is intended.
I can assure you that both are not typical in any part of this state
Does this mean
I can assure you that neither are typical in any part of this state
or does it mean
I can assure you that both are not typical in any part of this state. Maybe one or the other, but not both.
The former is more likely, but the latter is not unreasonable.
Confusion is also possible without a negative, but probably less common.
Both used in the negative means one of two and does not establish which of the two. Q: "Did you bring the suitcases?" A: "I couldn't carry both." Means I carried one of them, not the two of them. Sophey's Choice: Sophey could save one of her two children, but not both. She couldn't save both (one of the two).