Stars with planets at intermediate metallicities ([-0.7, -0.2] dex) exhibit properties that differ from the general field stars. Thirteen stars with planets reported in this metallicity range belong to the thick disc, while only one planet have been detected among stars of the thin disc. Although this statistics is weak, it contradicts the known correlation between the presence of planet and metallicity. We relate this finding to the specific property of the thin disc in this metallicity range, where stars are shown to rotate around the Galaxy faster than the Sun. Their orbital parameters are conveniently explained if they are contaminants coming from the outer Galactic disc, as a result of radial mixing. This must be considered together with the fact that metal-rich stars ([Fe/H]>+0.1 dex) found in the solar neighbourhood, which are the hosts of most of the detected planets, are suspected of being wanderers from the inner Galactic disc. It is then questionned why stars that originate in the inner and outer thin disc show respectively the highest and lowest rate of detected planets. It is suggested that the presence of giant planets might be primarily a function of a parameter linked to galactocentric radius, but not metallicity. Combined with the existing radial metallicity gradient, then radial mixing explains the correlation at high metallicity observed locally, but also the peculiarity found at low metallicity, which cannot be accounted for by a simple correlation between metallicity and planet probability.