Let $X$ be as smooth variety over a field $k$ of characteristic $0$.
Consider the following statements:
- The variety $X$ has no $k((t))$-rational points.
- No smooth compactification of $X$ has a $k$-rational point.
Are these equivalent? If not, what additional assumptions on $X$ would make them equivalent? I'm particularly interested in the case where $X$ is a homogenous space of a "nice" algebraic group over $k$.