Context.It has been hypothesized that the location of Herbig Ae/Be stars (HAeBes) within the empirical relation between the inner disk radius (r_in), inferred fromK-band interferometry, and the stellar luminosity (L_*), is related to the presence of the innermost gas, the disk-to-star accretion mechanism, the dust disk properties inferred from the spectral energy distributions (SEDs), or a combination of these effects. However, no general observational confirmation has been provided to date.Aims.This work aims to test whether the previously proposed hypotheses do, in fact, serve as a general explanation for the distribution of HAeBes in the size–luminosity diagram.Methods.GRAVITY/VLTI spectro-interferometric observations at ~2.2 μm have been obtained for five HBes representing two extreme cases concerning the presence of innermost gas and accretion modes. V590 Mon, PDS 281, and HD 94509 show no excess in the near-ultraviolet, Balmer region of the spectra (ΔD_B), indicative of a negligible amount of inner gas and disk-to-star accretion, whereas DG Cir and HD 141926 show such strong ΔD_Bvalues that cannot be reproduced from magnetospheric accretion, but probably come from the alternative boundary layer mechanism. In turn, the sample includes three Group I and two Group II stars based on the Meeus et al. SED classification scheme. Additional data for these and all HAeBes resolved throughK-band interferometry have been compiled from the literature and updated usingGaiaEDR3 distances, almost doubling previous samples used to analyze the size–luminosity relation.Results.We find no general trend linking the presence of gas inside the dust destruction radius or the accretion mechanism with the location of HAeBes in the size–luminosity diagram. Similarly, our data do not support the more recent hypothesis linking such a location and the SED groups. Underlying trends are present and must be taken into account when interpreting the size–luminosity correlation. In particular, it cannot be statistically ruled out that this correlation is affected by dependencies of bothL_*andr_inon the wide range of distances to the sources. Still, it is argued that the size–luminosity correlation is most likely to be physically relevant in spite of the previous statistical warning concerning dependencies on distance.Conclusions.Different observational approaches have been used to test the main scenarios proposed to explain the scatter of locations of HAeBes in the size–luminosity diagram. However, none of these scenarios have been confirmed as a fitting general explanation and this issue remains an open question.