How did Griffith experiments prove DNA is responsible for mice developing pneumonia?

Griffith's experiments involved injecting mice with different strains of Streptococcus pneumoniae. He observed that mice injected with the heat-killed virulent strain survived, while those injected with live non-virulent strains did not. Remarkably, when he mixed heat-killed virulent bacteria with live non-virulent bacteria, the mice developed pneumonia and died. This indicated that some "transforming principle" from the dead virulent bacteria was taken up by the live non-virulent bacteria, suggesting that DNA was responsible for the trait of virulence.