Experimental evidence both for and against a half-metallic ground state of the Heusler compound Co2FeSi has been published. Density-functional-theory-based calculations suggest a non-half-metallic ground state. It has been argued that on-site Coulomb interaction of the d electrons has to be taken into account via the LDA+U method, which predicts a half-metallic ground state for U approximate to 2.5,...,4.5 eV. X-ray magnetic linear dichroism (XMLD) can be used as a tool to assess the appropriateness of the LDA+U approach: The calculated spectra within the LDA+U or GGA+U schemes are different from those within the LDA or GGA. Due to its ability to separate different orbital symmetries, XMLD allows us to distinguish between different models of the electronic structure of Co2FeSi. In this article we discuss experimental XMLD spectra and compare them with detailed first-principles calculations. Our findings give evidence for the inadequacy of the LDA+U or GGA+U band structures, whereas constrained calculations with the GGA and a fixed spin moment of 6 mu(B) give better overall agreement between experiment and theory.