language exams - Do admissions care how close a TOEFL score is to the minimum?

I work with some students who will attend graduate school in the US. The schools they are applying for list minimum required TOEFL scores. Some have just reached the minimum scores required for admission to their schools of choice. Do admissions departments ever care about how close this number is to the minimum? In other words, will the students be at any greater advantage if they retake the test and get a higher score, or is the "score level met" simply a "met" or "not met" variable that goes into deciding whether or not the students are accepted?