Frank N. what Catherine Pawlick says does touch the surface of how a student becomes the student of a particular teacher, however having studied methodology in their course for foreign teacher for 2 years at the Vaganova Academy (a course which ended in 1995) I have a different take on it. If I may state my observations without offending anyone.
It is international ballet tradition that the teacher given most of the credit for a particular student is the one that a student has at the end of a program of study, prior to entering the professional world.
In Vaganova Academy, in most cases, the students work with three main ballet teachers. There, teachers are divided according to years of study. Teachers are placed, upon their graduation from the methodology course in a level that "suits" their proficiency to teach. Students generally stay with one teacher for 1st through 3rd year of study, another teacher for 4th and 5th year and yet another teacher for 6th, 7th, and 8th years of study. The lower level teachers 1-5 all have been educated and graduated to teach the Vaganova method by their methodology course for teachers (a five year course offered at this time only to Russian). Very few of the upper level teachers have completed this course. They are mostly teachers who have had a big career in Mariinsky, such as the late Zubkovskaya or the late Dudinskaya. How the classes will be divided now that the Academy has changed their program from 8 to 9 years of study is yet to be seen, as this is the first year!
The students begin the study of historic dance in the 1st year of study with a teacher. They stay with this historic dance teacher for 3 years. In 4th year they begin the study of character dance, which last for their remaining years of study at the academy with one teacher. In the sixth year of study they begin duet/partnering classes and continue this study for the remaining years of study in the Academy with one teacher. They are also offered acting classes in the 7th and 8th years of study, with one teacher. In the 8th year of study, the final year of historic dance is studied with the teacher of historic dance pedagogy (for teachers) who is an entirely different teacher from when the students where in 1st through 3rd years.
Please also recognize that while a teacher has responsibility for a class, the teacher is also working with them on pointe work (in the case of the ladies) and variations. Repetoire is staged by a completely different teacher and pas de deuxs are staged by two teachers, one male and one female. This is always the case. These classes meet everyday in the late afternoon into the evening.
How or why a particular teacher is given credit for a particular student is always different. In the case of Vishneva, Kovaleva was her teacher from 5th year on, if I recall correctly (sorry I arrived at the Academy when her class was in 6th year, so I am going by memories of too many years ago). Often it can be seen that a dancer will give a particular ballet master in the theatre credit as "their" teacher, instead of the final teacher in the Academy. As for the case of the dancer being discussed, I do not know the dancer, nor the teacher and as an outside observer, I question, in a polite manner, how a male teacher could ever be the teacher of a female dancer in Vaganova Academy? I am only going by the spelling of names, so I really do not know anything more.
That being said, it is obvious that the refinement and polish of the mature Mariinsky ballet dancer is a heartfelt labor of love for the teachers, all of them, recognized or not. In a perfect world all would be recognized but we are still working toward that perfection. I can tell you the mornings I sat observing the first class of the day of the 1st year students, how wonderful it was to see older students return, to greet their beloved first year teacher with gifts of flowers or just hugs. March 8th, Women's Day, was a day one would always see the children come in droves to pay homage to all of their teachers. The dancers know, but tradition is tradition.