Brightest Cluster Galaxies (BCGs) are typically massive ellipticals at the centers of clusters. They are believed to experience strong environmental processing, and their mass assembly and star formation history are still debated. We have selected three star forming BCGs in the equatorial field of the Kilo-Degree Survey (KiDS). They are KiDS 0920 (z=0.3216), KiDS 1220 (z=0.3886), and KiDS 1444 (z=0.4417). We have observed them with the IRAM-30m telescope in the first three CO transitions. We remarkably detected all BCGs at high signal-to-noise ratio S/N=~(3.8-10.2), for a total of 7 detected lines out of 8, corresponding to a success rate of 88%. This allows us to double the number of distant BCGs with clear detections in at least two CO lines. We have then combined our observations with available stellar, star formation, and dust properties of the BCGs, and we have compared them with a sample of 100 distant cluster galaxies with observations in CO. Our analysis yields large molecular gas reservoirs M_H2_=~(0.5-1.4)*10^11^M_{sun}_, excitation ratios r31=L'_CO(3->2)/L'_CO(1->0)_=~(0.1-0.3), as well as long depletion times {tau}_dep_=~(2-4)Gyr and high M_H2_/M_dust_=~(170-300) for the three targeted BCGs. The excitation ratio r31 of intermediate-z BCGs, including RX1532 and M1932 from previous studies, appears to be well correlated with the star formation rate and efficiency, which suggests that excited gas is found only in highly star forming and cool-core BCGs. By performing color-magnitude plots and a red sequence modeling we find that recent bursts of star formation are needed to explain the fact that the BCGs are measurably bluer than photometrically selected cluster members. To explain the global observed phenomenology we suggest that a substantial amount of the molecular gas has been accreted by the KiDS BCGs, but still not efficiently converted into stars. KiDS 1220 also shows a double-horn emission in CO(3->2) which implies a low gas concentration. The modeling of the spectrum yields an extended molecular gas reservoir of 9kpc, which is reminiscent of a mature extended-disk phase observed in some local BCGs.