There is no downside in applying directly for interviews. However, as stated, this is a red flag. In my experience, reasons for not being invited to an event are: lack of minimum qualifying criteria (e.g. GPA) or lack of “signals” from resume, cover letter, other experiences that person is indeed interested in consulting and in Bain.
those can be resolved and, as stated, are not always show stoppers for interview invitation.
hope it helps!