This still wouldn't be enough for people with diseases that cause major tremors, but I'd imagine it's enough for people who have lost fine motor control, because we're only trying to distinguish pushing from not-pushing.
Additionally, human touch sensation is incredibly good in the fingers, hypothesized to be related to our use of tools. That we can at all use such a touch screen is a miracle in the animal kingdom. Replacing this is not possible at this point in time as we age. However, larger and more clear buttons will help, along with a training period and good motivation for the person. As we age, we need to have the motivation to access the world and the opportunity to do so. The future requires all participants of every age.
A good place to start on the sources is here: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2563781/ . Let me know if you want a .pdf and cannot access the site past the abstract.
Chimpanzees can also use touch screens: https://www.youtube.com/watch?v=JkNV0rSndJ0
http://www.ted.com/talks/susan_savage_rumbaugh_on_apes_that_...
Skip to 15:52 if you want to go straight to the one playing Pac-Man.