The full-measure universality and strongly meager sets conjecture

A set $X\subset\mathbb{R}$ is full measure universal if every set of full Lebesgue measure contains an affine copy $\lambda X+t$ with $\lambda\in\mathbb{R}\setminus\{0\}$ and $t\in\mathbb{R}$. A set is strongly meager if $E+M\neq\mathbb{R}$ for every Lebesgue measure zero set $M$. Full-measure universality conjecture. The following assertions hold:

1. A set is full measure universal if and only if it is strongly meager.
2. If $X$ is a perfect set in $\mathbb{R}$, then $X$ is not full measure universal.

These assertions connect the measure-universality problem with the dual Borel viewpoint. The source states them as concluding conjectures and gives no resolution.