I think that the あっての in your example is different from the one in the dictionary.
悪気があっての回答 means “a reply given out of malice.” 悪気がある回答 means “a malicious reply.” The former describes the state of the person who made the reply, whereas the latter describes an attribute of the reply itself. So I would translate the two examples as
I did not reply (do the reply) out of malicious intent by any means.
Yes, ～あっての indicates an almost 100% dependency on the ～ part. My book defines it as 「～があるという条件があってはじめて～が可能」ということを強調する. Here are the accompanying examples that might make more sense:
愛あっての結婚生活だ。愛がなければ、一緒に暮らす意味がない。 → A marriage (lifestyle) depends completely on love. If there's no love, there's no point in living together.
私たちはお客様あっての仕事ですから、お客様を何より大切にしています。 → Ours is a job based entirely around our clients, so we always place the highest importance on them.
As for your examples, it's hard to tell the difference in the meaning. It's almost like the first one admits that it might have been somewhat malicious ("It is by no means a 100% malicious answer (but it might have been a little).") Whereas the second one seems like absolutely nothing about it was malicious at all. Tough call.