I take the view point that to be a personal student of some one then you really have to spend serious time with them and not just totally training. One on one, group classes, semi private's, going out to dinner, etc., etc., etc. Take Modern Arnis for example there are a small few people who were close to the Professor ie. more than a student but also a friend.
That group is in reality pretty small! Then there are a bunch of people who trained with him when he came around. Now attending his seminar's and training with him makes you a student but not in the same perspective as someone he went out to dinner with regularly, stayed at their house, etc., etc. I had the opportunity to train with him quite a few times and the opportunity for some one on one time but in
no way would I or should I consider myself a personal student! However his teachings and many of the instructors that he produced have greatly influenced me and for that I am forever grateful! Take for instance my own students that train with me weekly and are like family.
They are my personal students and those that have been around for a long time can use that designation. In another system like the Bujinkan when you get your Godan (5th Dan) you can put down that you are a personal/direct student of Hatsumi Sensei. You can do that and it is okay because in a way you are your own man/woman at that point and can chart in a way your own course.
However, are you really a personal student of Hatsumi Sensei? Meaning, do you train personally with him one on one? Does he even know your name? Have you eaten at his house or has he taken you out to dinner? Do you go on dog walks with him, can you call him for advice, etc., etc., etc. The personal student thing indicates or should indicate a very close relationship and it is way over used or misused by many people!
(just my 02. for what it is worth)