correlation implies dependency?

In this talk from prof Bernhard https://youtu.be/4qc28RA7HLQ?t=88

he only sees/shows linear correlation, and he assumes there is ‘dependency’?

Correct me if wrong but correlation does not imply ‘dependency’ so why is he implying it?

https://youtu.be/4qc28RA7HLQ?t=88

• Correlation does not imply causality, but dependence / independence is a different concept. Feb 1, 2020 at 15:19

From purely probabilistic perspective, if two random variables are correlated, they can't be statistically independent, i.e. $$\operatorname{cov}(X,Y)\neq0\rightarrow X\not\perp Y$$. But, if the correlation/covariance is $$0$$, those variables can still be dependent. So, presence of correlation implies dependence between random variables; but the presence of dependence doesn't imply correlation.