I think that it all really depends on the school and some of it seems sort of random at times. Different committees emphasize different components of the app, so I think that to a lot of schools your research experience may really mean the most to them. However, I can't say I know anything about the chances of getting in if you don't meet the minimum requirements. I do think that it's a really good thing that you have been in contact with that professor though because if they are willing to stand up for you in the committee meeting then that might make all the difference.