There was also an option on the list to explain your findings to the partner after the meeting and offer to draft an email for the client explaining your findings. From my personal experience that is what Partners seem to do when these situations occur, which they often do - why do you think HSF would assume that it’s better to present your findings in the meeting? At trainee level to me that seems risky and could cause an embarrassing situation for the trainee and create a bad impression on the client if anything is wrong (which it very possibly would be, as trainees are there to learn)
The wording of the scenario is clear - you know the answer. It doesn’t say “you think you know the answer” it says “you know the answer” and therefore you aren’t going to be “wrong”.
You are also getting too caught up in the detail not presented in the answer and assumptions of the worst case scenario. You are making an assumption that any approach to this would make the partner look bad - reality is that it would make the firm look good - it trains it trainees well enough that they know the detail.
The question is asking you for the most effective approach and the most effective approach is to give the client the answer in the meeting rather than following up afterwards, which requires more time from both your and the client’s perspective (all your time is chargeable - it’s wasted time following up on an answer you are not going to charge the client for, when you could charge it out to someone else). As mentioned above, this approach also fits HSF’s values - it wouldn’t necessarily be the right approach for other firms (like those mentioned by other posters where the partner would be horrified if you took this approach).