Equality of module sectional category and rational sectional category

Let $f\colon X\rightarrow Y$ be a map whose rationalisation $f_0$ admits a homotopy retraction. Let ${\rm secat}(f_0)$ denote the sectional category of the rationalisation and ${\rm msecat}(f)$ its module sectional category. Equality conjecture. One has

$${\rm msecat}(f)={\rm secat}(f_0).$$

The equality would identify the module and rational sectional categories for maps satisfying the stated rational homotopy-retraction hypothesis. The source presents this as a conjecture after noting examples where the hypothesis fails and the equality need not hold; no resolution is given.