The goal of Stack Exchange as a model of Q&A is to help as many people as possible. It's why we allow voting and collaborative editing, so that the community knowledge can be continually expanded, updated, and evaluated.
(The following is my opinion; others may disagree.)
With that goal in mind, I would say you should strike a balance. You should answer the OP directly, in that your answer should address any details or sub-questions included in the original question. If you have additional information that may be of use to a wider audience, however, do include it - but after you've answered the original question.
I'm assuming that the question you're referring to is the one asking for rabbit substitutes. I see nothing wrong with your answer after you updated it to explain why you think the saying holds some culinary truth. In this particular case, the OP did not say she was looking only for conventional or commercial solutions, did not specify in the question where she lives, and did not provide any parameters for what she considered an acceptable substitute other than texture and taste. You should not be expected to look beyond the question page to obtain the information needed to answer the question; someone mentioned that her location is listed on her profile, but looking at the profile is not, and never has been, a requirement for submitting an answer. Any pertinent details are expected to be in the question. You did nothing wrong by posting your answer.
This is a global community, and global perspectives are welcome and encouraged. Furthermore, the community should never assume anything about an asker's cultural, moral, geographic, or other situation unless the asker explicitly states them. (In this case, yes, the OP may life in the US, but the community has no way of knowing whether she perhaps immigrated from a country where cultural norms are drastically different from the US.)
To summarize: Address any specific scenarios mentioned in the original question, but do not be afraid to share additional knowledge to make your answer relevant to a wider audience. As long as it's relevant to the question, post it.