I fail to understand the rationale for that nagging message, as the chat room is seldom used and surely, as long as the conversation stays reasonably on topic of the parent post, it is better to keep discussion concerning the topic grouped with the topic itself. So why is there this rule?
See this for a general discussion of SE "ideals" regarding comments.
The idea seems to largely be that extended discussion that is only tangential to the question isn't very useful to have on a dedicated Q&A site. For instance, I remember there being a discussion on what counts as sexual assault in a question about the veracity of sexual assault statistics on a Skeptics.SE question, and this sort of thing tends to detract from the content of the answer or question itself.
It's fine to ask for clarification on ideas in the answer in the comments. (Although SE policy suggests that these things should be eventually edited in, or new questions should be asked.) Supposedly extended discussion might be better in chat (your mileage may vary on this) particularly when it's only between a few users (and the issues, while not outright tangential, might be beside the point of the question), for reasons similar to why having many tangentially related comments isn't the best thing.
To be fair, I've seen a generally more permissive attitude towards commenting on the main sites I participate in, for instance, with humorous side-comments or with very anecdotal "this sounds about right" comments that aren't completely necessary. But it's probably permitted with the caveat that it shouldn't be allowed to turn into a full-blown, off-topic conversation.