Hi there,
I like this question quite a lot. It addresses a major missconception about the interview process.
While companies try to "standardize" the recruiting process and to make as objective / quantitative as possible, the reality is that an interview is a highly personal experience.
Let me elaborate. You usually make your mind about liking someone in the first 5 minutes of meeting that person. If you make a great impression you basically just need to solidify that impression for the rest of the interview. However if you cause a poor first impression you will need to convince the interviewer otherwise during the rest of the interview (much harder!)
Now, why is this relevant? If you dont focus on the FIT / how you actually come across you are actually missing on a great opportunity to start strong.
Furthermore, the process to make hiring decisions is usually much broader than simply how did you do a given case.
I was involved in several hiring decisions where I was dicussing with senior partners, and trust me that case details rarely came up (at least how you would expect it!)
To make a long story short, start preparing PEI from the get go and ensure you are letting a strong impression since the very few minutes.
My 2 cents