Is it true that scientists proved that DNA controls traits through experiments with bacteria?

DNA was proven to be the heritable material through the use of bacteria and a specific type of bacterial virus called bacteriophage. The control of traits would then be something easily deduced from this through the years of work with plants and model organisms like drosophila.Is it true that scientists proved that DNA controls traits through experiments with bacteria?
I don't know how they originally proved it, but they can prove it now with gene slicing and with the glow-in-the dark moneky they made.