We explore the link between solar energetic particles (SEPs) observed at 1 AU and large-scale disturbances propagating in the solar corona, named after the Extreme ultraviolet Imaging Telescope (EIT) as EIT waves, which trace the lateral expansion of a coronal mass ejection (CME). A comprehensive search for SOHO/EIT waves was carried out for 179 SEP events during Solar Cycle 23 (1997-2006). 87% of the SEP events were found to be accompanied by EIT waves. In order to test if the EIT waves play a role in the SEP acceleration, we compared their extrapolated arrival time at the footpoint of the Parker spiral with the particle onset in the 26 eastern SEP events that had no direct magnetic connection to the Earth. We find that the onset of proton events was generally consistent with this scenario. However, in a number of cases the first near-relativistic electrons were detected too early. Furthermore, the electrons had in general only weakly anisotropic pitch-angle distributions. This poses a problem for the idea that the SEPs were accelerated by the EIT wave or in any other spatially confined region in the low corona. The presence of weak electron anisotropies in SEP events from the eastern hemisphere suggests that transport processes in interplanetary space, including cross-field diffusion, play a role in giving the SEPs access to a broad range of helio-longitudes.