  Ab initio calculations of QED radiative corrections to the $^2P_{1/2}$ -
$^2P_{3/2}$ fine-structure transition energy are performed for selected F-like
ions. These calculations are nonperturbative in $\alpha Z$ and include all
first-order and many-electron second-order effects in $\alpha$. When compared
to approximate QED computations, a notable discrepancy is found especially for
F-like uranium for which the predicted self-energy contributions even differ in
sign. Moreover, all deviations between theory and experiment for the
$^2P_{1/2}$ - $^2P_{3/2}$ fine-structure energies of F-like ions, reported
recently by Li et al., Phys. Rev. A 98, 020502(R) (2018), are resolved if their
highly accurate, non-QED fine-structure values are combined with the QED
corrections ab initially evaluated here.
