We investigated the magnetic properties of individual Ho atoms adsorbed on the (111) surface of Pt, which have been recently claimed to display single ion magnetic behavior. By combining x-ray absorption spectroscopy and magnetic dichroism measurements with ligand field multiplet calculations, we reveal a ground state which is incompatible with long spin relaxation times, in disagreement with former findings. A comparative study of the ground state and magnetic anisotropy of Ho and Er on Pt(111) and Cu(111) emphasizes the different interaction of the 4f orbitals with localized and delocalized substrate states. In particular, we find a striking rotation of the magnetization easy axis for Er, which changes from out of plane on Pt(111) to in plane on Cu(111).