We studied the impact of the revisited values for the LSR circular velocity of the Milky Way (Reid et al. 2004) on the formation of the Magellanic Stream. The LSR circular velocity was varied within its observational uncertainties as a free parameter of the interaction between the Large (LMC) and the Small (SMC) Magellanic Clouds and the Galaxy. We have shown that the large–scale morphology and kinematics of the Magellanic Stream may be reproduced as tidal features, assuming the recent values of the proper motions of the Magellanic Clouds (Kallivayalil  2006). Automated exploration of the entire parameter space for the interaction was performed to identify all parameter combinations that allow for modeling the Magellanic Stream. Satisfactory models exist for the dynamical mass of the Milky Way within a wide range of 0.6 ⋅ 1012 M⊙ to 3.0 ⋅ 1012 M⊙ and over the entire 1–σ errors of the proper motions of the Clouds. However, the successful models share a common interaction scenario. The Magellanic Clouds are satellites of the Milky Way, and in all cases two close LMC–SMC encounters occurred within the last 4 Gyr at t < −2.5 Gyr and t ≈ −150 Myr, triggering the formation of the Stream and of the Magellanic Bridge, respectively. The latter encounter is encoded in the observed proper motions and inevitable in any model of the interaction. We conclude that the tidal origin of the Magellanic Stream implies the previously introduced LMC/SMC orbital history, unless the parameters of the interaction are revised substantially.