Like PodZilla said, I would base my two cents on this logic: The schools just need to have two of the three before the interview so they can glance at them quickly. I think I saw your post earlier on another thread that you have already applied, so right now you are awaiting the interview invites. Do you have your MCAT scores yet? If so then really that is the more important statistic they need. In my opinion, I bet they could care less about having all three before the interview but would like to have at least one from the podiatrist and one from a professor before the interview.
I doubt that an interview acceptance varies whether they have all the LORs or not, unless you are a sub 3.0 student with an MCAT under 20. They want to get you interviewed as quickly as possible and most schools probably want you to be the 2nd or 3rd school you interview with so that they can lure you in quicker than not.
SIDE NOTE: One of the issues with MD, DO, Podiatry, and every other field of medicine is that the first month their application cycle begins is the longest it will take to get verified. I know last year, people who submitted their application on the first day of the cycle got verified just a day or two earlier than someone who finished their application on the 18th day of the cycle. For MD and DO school my classmates told me that people have everything ready on day 1 to submit. It really isn't the same with podiatry because not everybody has their MCAT in by the first week of August, while almost every med school applicant I know of has everything ready by the first week of June or had at least taken the MCAT by early June and are just a week or two behind. In the podiatry school application cycle, there isn't that much of a rush like there is for MD or DO school. Podiatry school application cycle is from early August to late April (and sometimes if there are candidates that get their DO or MD school rejections they apply to podiatry school in May and still get in). While MD or DO school their application cycle is strict and lasts from June to October, November. From what a friend told me there is a major difference in the chance of getting accepted to an MD or DO school if you apply on June 1st vs. July 1st, while for podiatry school they are essentially the same.
I am very opinionated!