The large metal object you touch needs to be grounded so it can dissipate any static charge, touching a random metal object which is not grounded will not help.
What I do is put the PSU in the case first and connect it up to the mains supply, if it has its own on/off switch it can be left off. By doing this the whole case is earthed/grounded during your build. I then install all components without plugging in the power cables from the PSU into any component. Once everything is in the case I discharge myself by touching the case one last time and then disconnect the PSU from the mains supply. Then without moving about too much to minimise any chance of static build up I plug in all the PSU cables to all the components, once done then plug the PSU back into the mains and the whole system is grounded.
It has worked for me and never had a problem.