Let $(M,g)$ be a Riemannian manifold. Let $S_g$ be the corresponding Sasaki metric on $TM$. For every $V_p\in TM$, is it obvious that $0_p$ is the closest point of  the zero section to $V_p$?

With some abuse of terminologies a rephrase of the question would be:  Is the height of a rigth  triangle shorter than its hypotenuse?