Like the video linked by
@presta shows, the bead does not stretch and has a smaller diameter than the outer edge of the rim but a larger diameter than the well of the rim. If the bead is too tight to go over the rim without being fully into the well (where it is already "in the rim"), then no tool or lever is going to get the last bit of bead over the rim unless it pulls the rest of the bead firmly into the well but once you know that, you don't need a special tool/lever.
Having said that, difference in tolerances make some rim/tyre combinations more difficult than others and sometimes grip or purchase on the tyre etc. can be lacking, and hands and skin can be delicate (I suffer from eczema and often have skin thinned by steroids and lubricated with moisturising cream) and a tool or lever can make a difference.
