Hi! I'm new here, so I hope you don't mind me jumping in on this conversation. This is an ongoing issue that I see with my students, particularly if they are nervous, brand-new to the piano, or lacking muscle tone in their fingers. I have also noticed that a lot of students feel it is necessary to "strike" the keys rather than press in. I have done a few things to counteract what I have termed "finger gymnastics":
1.) Ongoing reminders. "No finger gymnastics!" and of course they giggle... and whether it does any good or not depends on how how determined they are to fix that problem.
2.) I have given them exercises to work on legato notes, with their fingers "glued" to the keys. Slowly, carefully, five-finger scales, encouraging them to press in and feel it fall rather than hit it like their fingers are hammers.
3.) I have gone so far as to tape a students fingers to the piano. This has to be done with the right kind of student - this one is game for anything and she thought it was hilarious. "Mom! She taped my fingers to the keys!" "Oh good, that might actually help!" came the response. It wasn't done out of frustration, but the little girl (she's only six, so likely much smaller than your 10 year old student) actually requested today that I tape her fingers down again because she was getting so frustrated. I just reminded her to relax her fingers and keep her spider fingers up.
4.) I have also noticed that student who tend to have flat, tense fingers also struggle with correct fingering on the notes and hit the note with whatever finger happens to land there. This is where I get them to slow down again. But anyway, that was a side note.... the next thing I do is watch to see whether their wrist is hitting to wood beneath the keys or if their shoulders are tense. If this one little girl I referenced before has particularly tense shoulders, her entire arm and hand positioning will reflect that tension. So I remind her to take a deep breath, sit up straight, keep her shoulders relaxed and square, and to play slowly and carefully.
5.) I don't know how "hands on" you are comfortable with being when you are teaching, but I have also kept my hands on their wrists (gently) and pulled the wrists upward and keep them held there while they play. That also seems to help, but, again, it depends on the student.
Also, you say the knuckles "collapse"? I wonder if she is double-jointed? Mine did that on occasion, and I think maybe your suggestion of a stress ball might help... I had to develop really good technique before my fingers stopped doing that. Perhaps encourage her to push her fingers forward so she is playing right on the tips and maximizing the use of her finger muscles.... maybe she is playing too far back on the pads of her fingers.
I do agree with you that technique is very important, but I have to add that if she enjoys the music and you emphasize the musicality of the piece rather than technique (though I do remind my students of proper technique each lesson if it is an ongoing issue) she will likely stick with it a little more... since she is older, I hesitate to push too much in the way of technique rather than music appreciation and enjoyment, as she may end up feeling like she can't do it and give up.

Good luck!