But it seems I should have used the present imperfective "отвечаем" here. What is the grammatical rationale for this?
This is an excellent question.
Yes, you should have used ''отвечаем,'' but the following sentence sounds perfectly okay: ''О, думаю, тебе и так уже известно, но если во время рыбалки ты допустишь ошибку и погибнешь, то мы за это не понесем ответственность.''
As you see, here I used the perfective ''понесем ответственность''. With this perfective, this sentence sounds absolutely natural. With ''не несем ответственность'' it would sound fine, too. But with ''не ответим'' it sounds weird!
So why does ''не ответим'' sound bad, while ''не понесем ответственность'' sounds fine despite that both forms are perfective?
The reason is connected with a connotation of the perfective expression ''ответить за что-либо'': Historically, this expression (in the perfective form) was a colloquial expression used by semi-criminals and criminals in the 1990s as a threat, e.g., ''за базар ответишь'' (''you will be held responsible for you words,'' ''you will pay for your words''). ''Отвечать за что-либо'' does not have a criminal connotation and simply means ''to be responsible for something.'' ''Понести ответственность за что-либо'' does not have a criminal connotation either, although is basically equivalent to ''ответить за что-либо'' in terms of the essence of the meaning - ''someone has been held responsible for something.''
Nowadays the expression ''ответить за что-либо'' is often used by general public, too, but still has some criminal flavour. For example, the expression ''ты ответишь за это'' is perceived as a threat or a promise to retaliate, i.e., something like ''I will make you pay for that.''
Moreover, the negation of this phrase, i.e, ''я за это не отвечу,'' is practically not used, although is not ungrammatical or wrong in any way. If you google the exact phrase "я за это не отвечу," you will get only a few results, but all these results obviously come from native speakers. The meaning is rather, ''I will get away with that,'' or, ''You will be unable to make me pay for that.'' The criminal flavour is still there.
In short, the usage and flavour of ''ответить за что-либо'' (in the perfective form) do not fit your situation.