Free rotation of sigma bonds; diastereomer formation; thermodynamic and kinetic products
You have only considered reaction from the s-trans conformation of 1,3-butadiene, where the 2 double bonds are in a cis relationship about the central single bond.  The s-trans conformation is in equilibrium with the s-cis conformation.  The s-cis conformation can react also react to the terminal olefin, but also  (by the mechanism you described) it can react to produce the z 2-butene as one of its kinetic products.  Hence, all 3 butenes (1-butene and e and x 2-butene) can be formed as the kinetic products.