Context.The quasar class of extreme Population A (xA) (also known as super-Eddington accreting massive black holes, SEAMBHs) has been hailed as potential distance indicators for cosmology.Aims.The aim of this paper is to define tight criteria for their proper identification, starting from the main selection criterionR_FeII > 1, and to identify potential intruders that do not meet the selection criteria, which nonetheless have been selected as xA because of the coarseness of automatic searches. The inclusion of the spurious xA sources may dramatically increase the dispersion in the Hubble diagram of quasars, which were obtained from virial luminosity estimates.Methods.We studied a sample of 32 low-zquasars that were originally selected from the seventh data release of the Sloan Digital Sky Survey as xA or SEAMBHs, which have been proved to be almost certainly misclassified sources. All of them show moderate to strong Fe IIemission and the large majority show strong absorption features in their spectra which are typical of fairly evolved stellar populations. We performed a simultaneous fit of a host galaxy spectrum, active galactic nucleus (AGN) continuum, FeII template, and emission lines to spectra, using the fitting technique based onULySS, the full spectrum fitting package. We derived the main accretion parameters (i.e., luminosity, black hole mass, and Eddington ratio) and investigate the relation between host galaxy properties and AGN.Results.For sources in our sample with spectral types that correspond to a relatively low Eddington ratio, we find an overall consistency between Hβ_NC, [O III]λλ4959,5007 line shifts, and the mean stellar velocity obtained from the host galaxy fit (within ≲|60| km s⁻¹). Only one source in our sample qualifies as a xA source.Conclusions.The correct classification of spectra that were contaminated by heavy absorption requires careful determination of the host galaxy spectrum. Contamination and misclassification are not usual in the identification of the xAs, nor at lowzor at highz. We find a high fraction of host galaxy spectrum; in half of the sample this is even higher than 40%. When absorption lines are prominent, and the fraction of the host galaxy is high, host galaxy spectrum mimics FeII, which may result in a mistaken identification of FeII spectral features. We have identified several stellar absorption lines that, along with the continuum shape, may lead to an overestimate ofR_FeII, and therefore to the misclassification of sources as xA sources.