Actually, in my opinion, there is huge misunderstanding today in quantum mechanics. I can not see the difference between De Broglie's formula and Heisenberg's uncertainty principle. If someone understands that, then your question is answered!
I have seen this paper a long time ago. If you want to verify Born's rule, you have to solve Schrodinger's equation and compare the theoritical results with experimental results. This is not happening in that paper.
That's why I believe that Born's rule is not verified and even more that it...
I really would like to see the maths and the corresponding experiment that verifys Born's rule. Newton's laws can easily be verified in any common university's laboratory. It 's not the same.