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.