We present an analysis of the significantly expanded HARPS 2011 radial velocity data set for GJ 581 that was presented by Forveille et al. (2011). Our analysis reaches substantially different conclusions regarding the evidence for a Super-Earth-mass planet in the stars Habitable Zone. We were able to reproduce their reported chi_{ u}^2 and RMS values only after removing some outliers from their models and refitting the trimmed down RV set. A suite of 4000 N-body simulations of their Keplerian model all resulted in unstable systems and revealed that their reported 3.6sigma detection of e=0.32 for the eccentricity of GJ 581e is manifestly incompatible with the systems dynamical stability. Furthermore, their Keplerian model, when integrated only over the time baseline of the observations, significantly increases the chi_{ u}^2 and demonstrates the need for including non-Keplerian orbital precession when modeling this system. We find that a four-planet model with all of the planets on circular or nearly circular orbits provides both an excellent self-consistent fit to their RV data and also results in a very stable configuration. The periodogram of the residuals to a 4-planet all-circular-orbit model reveals significant peaks that suggest one or more additional planets in this system. We conclude that the present 240-point HARPS data set, when analyzed in its entirety, and modeled with fully self-consistent stable orbits, by and of itself does offer significant support for a fifth signal in the data with a period near 32 days. This signal has a False Alarm Probability of <4% and is consistent with a planet of minimum mass of 2.2 Earth-masses, orbiting squarely in the stars Habitable Zone at 0.13 AU, where liquid water on planetary surfaces is a distinct possibility
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