  (Abridged) We have investigated the reliability of the widely used I-band Tip
of the RGB relative distances for a sample of Local Group galaxies with complex
Star Formation Histories (SFR) and Age Metallicity Relationships (AMR) namely
the LMC, SMC and LGS3. The use of the K-band is also discussed. By employing
theoretical stellar population synthesis techniques, we find that using actual
determinations of SFR and AMR of the LMC and SMC, their RGB is populated by
stars much younger (by 9 Gyr) than the Galactic globular cluster counterparts,
on which the I-band (and K-band) TRGB absolute magnitude is calibrated. This
age difference induces a bias in both the photometric metallicity estimates
based on the comparison of RGB colours with globular cluster ones, and the TRGB
distances. The extent of the distance bias is strongly dependent on the
specific TRGB technique applied, and on the assumed I-band BC scale adopted;
the correction to apply to the SMC-LMC distance modulus ranges from 0 up to
+0.10 mag. LGS3 is an example of galaxy populated mainly by old stars, so that
photometric metallicity and distance estimates using globular cluster
calibrations are reliable. However, the relative distance moduli between
Magellanic Clouds and LGS3 are affected by the population effects discussed for
the LMC and SMC. The corrections to apply to the K-band TRGB distances are
larger than the I-band case. Our results clearly show that the presence of a
well developed RGB in the CMD of a stellar system with a complex SFR does not
guarantee that it is populated by globular cluster-like red giants, and
therefore the TRGB method for distance determination has to be applied with
caution.
