You are right, but the tendency of the doubly negated sentence is to soften the final claim. Often this happens out of modesty or false modesty. Much like these English phrase:
Not unfamiliar, not unrelated, not unheard of
If I had to give a rule for this complicated and situational phenomenon, I would advise to replace the double negated claim A by a statement slightly more moderate than A. In some cases though, the statement is absolute and can't be softened. These cases, however, account but for a tiny fraction of double negatives:
Frau Lu hier ist noch unverheiratet!
Nein, ich bin nicht unverheiratet!
here, the phrasing was prompted by previous sentence. Furthermore, consider this list:
Nicht unverheiratet = verheiratet
Nicht unmöglich ~ möglich, tendenziell unwahrscheinlich
Nicht unerheblich ~ erheblich oder nicht zu vernachlässigen
Nicht unerfahren ~ erfahren, meist bescheiden gemeint
Nicht unansehnlich ~ ansehnlich, meist ein Versuch unbeeindruckt zu wirken
Let's say, Miss Zuo finds Mister Lu attractive. Miss Pumbelchuke is aware of it and wants to embarrass her. Miss Zuo might state:
Er ist nicht unansehnlich.
This allows her to retain some aloofness. Generally, the connotation is quite different from:
Er ist ansehnlich.
and comes close to
Er ist ganz ansehnlich. ,
where ganz considerably softens the claim. Unfortunately, with nicht unerheblich you picked a much harder and more situational case. Fundamentally, I would interpret nicht unerheblich as a softening as well. It could well appear in the context of wanting to soften an accusation:
Herr Pervatender, Sie haben durch Ihre nicht gerade ungefährlichen Spekulationen unserer Firma nicht unerheblichen Schaden zugefügt.
To me, it's much easier (less brave) to voice these, than the direct counterparts. On the other hand, such softening is reminiscent of elaborate or formal speech. So it might intimidate some people even more. That's how I interpret the comment by npe. Yet, I would be much, much more intimidated by the direct accusation.