The HST proper motion (PM) measurements of the Clouds have severe implications for their interaction history with the Milky Way (MW) and with each other. The Clouds are likely on their first passage about the MW and the SMC's orbit about the LMC is better described as quasi-periodic rather than circular. Binary L/SMC orbits that satisfy observational constraints on their mutual interaction history (e.g., the formation of the Magellanic Bridge during a collision between the Clouds ~300 Myr ago) can be located within 1σ of the mean PMs. However, these binary orbits are not co-located with the Magellanic Stream (MS) when projected on the plane of the sky and the line-of-sight velocity gradient along the LMC's orbit is significantly steeper than that along the MS. These combined results ultimately rule out a purely tidal origin for the MS: tides are ineffective without multiple pericentric passages and can neither decrease the velocity gradient nor explain the offset stream in a polar orbit configuration. Alternatively, ram pressure stripping of an extended gaseous disk may naturally explain the deviation. The offset also suggests that observations of the little-explored region between RA 21h and 23h are crucial for characterizing the full extent of the MS.