If possible before interviewing try to find information about the personality type/mannerisms of the interviewer. Is he or she quiet and soft spoken, loud and constantly talking, some mixture, etc? Also, find out whether the interviewer speaks quickly, slow and deliberative, some combination, etc. Once armed with this information, you can tailor your delivery accordingly, and if comfortable mirror the person to the extent possible.
LegalJob is not advising you to change who you are but just to be more aware. It may take minimal effort to tweak your delivery a bit so that you do not appear obviously out of sync with the interviewer. If he or she is a fast talker and you are slow and deliberate that could be a painfully long interview for that person. People generally enjoy talking to people that are like them so know that and plan accordingly. Your style of speech may not be the intangible that gets you into the big firm but it could be the reason you get rejected.