It's absolutely correct to use both perfective and Imprefective after НЕ. Look at the following examples: Я не понял, что он сказал. (It's a particular situation, perfective means 'once'.) Я (никогда) не понимал, почему люди изучают иностранные языки. (The situation in general + never which expresses a habit.) Он не написал мне письма (я не получил от него конкретного письма, которого я ждал). Он не писал мне писем (нескольких писем, никогда).

I guess it was wrong suggestion that negatives go against the nature of perfective verbs. Forget about it. Probably it is just a misunderstanding. Might you give us examples of the rule? Where did you get it?

"Я не понял" или "Он не написал мне письма" = it's absolutely correct, good Russian.

"не" doesn't deny completion, it denies the action itself, either it was completed or not. Perfective verbs describe actions that are complete OR were/will be made once. Look at Tati's examples, if they are not clear enough, I would be glad to provide further explanations.

They did not think such as it was. Nobody understand it such at all. So anybody did not understand it at all.