The path towards robust near-infrared extensions of stellar population models involves the confrontation between empirical and synthetic stellar spectral libraries across the wavelength ranges of photospheric emission. [...] With its near-UV to near-IR coverage, the X-shooter Spectral Library (XSL) allows us to examine to what extent models succeed in reproducing stellar energy distributions (SEDs) and stellar absorption line spectra simultaneously. This study compares the stellar spectra of XSL with the PHOENIX spectra of the Gottingen Spectral Library. The comparison is carried out both separately in the three arms of the X-shooter spectrograph, and jointly across the whole spectrum. When adopting the stellar parameters published with data release DR2 of XSL, we find that the SEDs of the models are consistent with those of the data at Teff > 5000 K. Below 5000 K, there are significant discrepancies in the SEDs. When leaving the stellar parameters free to adjust, satisfactory representations of the SEDs are obtained down to about 4000 K. However, in particular below 5000 K and in the UVB spectral range, strong local residuals associated with intermediate resolution spectral features are then seen; the necessity of a compromise between reproducing the line spectra and reproducing the SEDs leads to dispersion between the parameters favored by various spectral ranges. We describe the main trends observed and we point out localized offsets between the parameters preferred in this global fit to the SEDs and the parameters in DR2. These depend in a complex way on position in the HR diagram (HRD). We estimate the effect of the offsets on bolometric corrections as a function of position in the HRD and use this for a brief discussion of their impact on the studies of stellar populations. [abridged]
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