Aims. The nearby, bright, almost completely unreddened Type Ia supernova 2011fe in M101 provides a unique opportunity to test both the precision and the accuracy of the extragalactic distances derived from SNe Ia light curve fitters. Methods. We applied the current, public versions of the independent light curve fitting codes MLCS2k2 and SALT2 to compute the distance modulus of SN 2011fe from high-precision, multi-color (BVRI) light curves. Results. The results from the two fitting codes confirm that 2011fe is a "normal" (not peculiar) and only slightly reddened SN Ia. New unreddened distance moduli are derived as 29.21 ± 0.07 mag (D ∼ 6.95 ± 0.23 Mpc, MLCS2k2), and 29.05 ± 0.07 mag (6.46 ± 0.21 Mpc). Conclusions. Despite the very good fitting quality achieved with both light curve fitters, the resulting distance moduli are inconsistent by 2σ. Both are marginally consistent (at ∼1σ) with the Hubble Space Telescope key project distance modulus for M101. The SALT2 distance is in good agreement with the recently revised Cepheid-and TRGB-distance to M101. Averaging all SN-and Cepheid-based estimates, the absolute distance to M101 is ∼6.6 ± 0.5 Mpc.