Several star clusters show a roughly flat velocity dispersion profile at large radii, which is not predicted from self-consistent models with a tidal truncation (such as `King models'). This non-zero temperature of stars has previously been attributed to deviations from Newtonian gravity in the weak acceleration regime, but it could also be due to an additional (dark matter) component. We investigate the kinematics of stars near the edges of globular clusters assuming Newtonian dynamics and considering collisional N-body dynamics in different (tri-axial) galactic tidal fields. The flattening of the velocity dispersion can be explained by stars within the tidal radius of the cluster that have an energy slightly in excess of the critical energy of escape. Due to tri-axial shape of the Roche volume, their timescale of escape is long enough to have a measurable effect on the kinematics in the outer parts of the cluster. We derive a scaling for the velocity dispersion of these stars, as a function of clusters mass, which is remarkably close to what modified Newtonian dynamics predicts: v_rms ~ M^1/4. However, there is an additional dependence on the details of the orbit of the cluster around the galaxy centre, which can be used to discriminate between the scenarios and looked for in clusters at different galactocentric radii. Not including these stars when modelling globular cluster kinematics with equilibrium (self-consistent) models, can lead to a false detection of a dark matter halo, or misinterpretation of the underlying gravity law.