Hmm... I thought I'd give a student's perspective. Aside from doing pole, I am also a student in aerial silks, lyra and static trapeze and I have hyperextended elbows too. I've never done ballet so I cannot speak for that, but for pole and aerial, I don't see my hyperextended elbows as a "problem" or a "habit" that necessarily needs correction. I'm always open to my teachers' suggestions on form, but we all agree that I should lock my elbows if it makes me feel safer.
When I was learning how to hand stand on the pole, I was able to do it easily and securely with locked (but crooked) elbows. I kept being instructed to straighten them into "proper form", and I fell on my head each time. I was frustrated that I could no longer keep up with my class. I was quite annoyed for being repeatedly called out on my elbows. I felt it was unfair for my teacher to force me to lose that "brace". We couldn't figure out why, so she finally pulled me aside and watched me do it successfully my way, then observed how I fell each time I did it her way. We both had a lightbulb moment -- it's not that I was weaker than everyone else in class (I can hold my chatarungas just as long), but it's that my body dynamics are just different. I figured out how to muscle my way into bending my elbows look straight after I learned to balance in a handstand with crooked elbows, but I still choose to do it with hyperextended because that's what feels right to me. We went through this again when I was learning the butterfly and the bow and arrow which both need locked arms. But these times my teacher worked with me to find the best way that fit my body instead of having me muscle my way into the appearance of straight arms.
My aerial teachers work together with me on my elbows too. There are certain moves in lyra where I intuitively grip the ring palm up or palm down differently from the way we're taught, and that's cool as long as I have tried both ways and I am confident that I am more stable doing my way. In fact, none of my aerial teachers ever saw my elbows as a problem... One of them even celebrates them and finds funky poses for me on the silks where I can utilize my elbows to freak people out :P I felt good the first time she did that because it was the first time I saw them as an asset instead of a disadvantage, which was the way I was made to feel about them before :)
So far, I have thankfully never injured myself because of my elbows. I've only injured myself when I have been asked to rigidly stick to the norm despite raising my concerns. Intuition tells you when something feels wrong, and in the end, it's only the student herself who can know that. My advice is for you listen to your student and encourage her to communicate how her body feels every time she does something differently because of her elbow dynamics. Ask her to try both the usual way and her way, see where she feels better, then work with her to find the safest way regardless of her elbow position. I promise if you do this, she'll grow as a dancer and love you for your guidance :)
