Hand sanitizer kills off a large quantity of bacteria, the ones that are left then have no competition for resources and your typical bacterial generation is 20 minutes or so. If you use the Hand Sanitizer you are making the resistant bacteria more likely to reproduce. Hence all you are doing is growing strong bacteria.

Welcome to how MRSA and other resistant diseases came about. They wouldn't be out like they are now if we didn't get so picky about how clean we make everything. We just keep giving them more and more room to reproduce in.