It's a matter of emphasis, in this case you want to emphasize the action and not the result, eitherways, in this case you can choose either option subjectively depending on the message you want to convey.
I believe you can always use Genitive for objects of negated verbs. At least I can't think of a situation when it's impossible.
I also found this bit on Wikipedia:
Use of genitive for negation is obligatory in Slovene, Polish and Old Church Slavonic. The East Slavic languages (Russian, Ukrainian, and Belorussian) employ either the accusative or genitive for negation, albeit the genitive is more commonly used. In Czech, Slovak and Serbo-Croatian, negating with the genitive case is perceived as rather archaic and the accusative is preferred, but genitive negation in these languages is still not uncommon, especially in music and literature.
It seems it's not wrong, just not preferred. From what I've read here, it seems that the genitive case is preferred in negative sentences, while accusative is preferred when it's not negative. However, both are okay.
Someone's post has a link to a Wikipedia article talking about that. It's pretty similar to how Portuguese uses a genitive preposition to say "about" ("falar de" instead of "falar sobre").
Is "сказал" more idiomatic here? Is there any important difference in this case?
Both work, with a slight difference in meaning.
«Я этого не говорил» is imperfective, it represents not saying for some period of time (perhaps never). It works better for phrases you never intended to say.
The imperfective verb говорить represents action that has beginning and end. Negated, it represents not saying something for some period of time, a continuous not-saying.
«Я этого не сказал» is perfective: it means you didn't say something in a particular situation, at some paticular time. This works better for phrases you were planning to say, or should have said, but haven't. I.e. you had an opportunity to say something but you missed it, you didn't say something at some moment of time.
The perfective verb сказать represents a single, momentary action, that happens during a moment of time. Negated, it represents not saying something at some point of time, i.e. missing some chance to say something.
"I was not saying that" was my translation, which I think is just as correct as yours.
That's a bit off.
First, the verb in the exercise--говорил--is masculine past tense, and the approximate English transcription of the pronunciation would be gah-vah-REEL.
Second, the first person present tense would be говорю, which would be pronounced gah-vahr-YU.
Third, don't confuse the Russian letter в with the Latin letter b; they are not the same consonant. Russian в = Latin v, and Russian б = Latin b.