We provide a new interpretation of ultraviolet transition region emission line widths observed by the SUMER instrument on the Solar and Heliospheric Observatory (SOHO). This investigation is prompted by observations of the chromosphere at unprecedented spatial and temporal resolution from the Solar Optical Telescope (SOT) on Hinode revealing that all chromospheric structures above the limb display significant transverse (Alfvenic) perturbations. We demonstrate that the magnitude, network sensitivity and apparent center-to-limb isotropy of the measured line widths (formed below 250,000K) can be explained by an observationally constrained forward-model in which the line width is caused by the line-of-sight superposition of longitudinal and Alfvenic motions on the small-scale (spicular) structures that dominate the chromosphere and low transition region.