Quantitative comparisons are presented between gyrokinetic simulations and experimental values of the carbon impurity peaking factor in a database of JET H-modes during the carbon wall era. These plasmas feature strong NBI heating and hence high values of toroidal rotation and corresponding gradient. Furthermore, the carbon profiles present particularly interesting shapes for fusion devices, i.e., hollow in the core and peaked near the edge. Dependencies of the experimental carbon peaking factor (R/L-nC) on plasma parameters are investigated via multilinear regressions. A marked correlation between R/L-nC and the normalised toroidal rotation gradient is observed in the core, which suggests an important role of the rotation in establishing hollow carbon profiles. The carbon peaking factor is then computed with the gyrokinetic code GKW, using a quasi-linear approach, supported by a few non-linear simulations. The comparison of the quasi-linear predictions to the experimental values at mid-radius reveals two main regimes. At low normalised collisionality, nu*, and T-e/T-i < 1, the gyrokinetic simulations quantitatively recover experimental carbon density profiles, provided that rotodiffusion is taken into account. In contrast, at higher nu* and T-e/T-i > 1, the very hollow experimental carbon density profiles are never predicted by the simulations and the carbon density peaking is systematically over estimated. This points to a possible missing ingredient in this regime.