What is an empirical proof that two concepts are not independent/orthogonal?
Since the data show a two-way dependence (low A -> low B, hi A -> hi B and the reverse) this would prove the variables are not independent, as 


  Linearly independent, orthogonal, and uncorrelated are three terms used to indicate lack of relationship between variables. 


Reference
- Rodgers et al., The American Statistician (1984); 38(2): 133-4