Griffith did not know about DNAs role as hereditary material at the time of his experiment. All he observed was bacteria gaining new traits from dead bacteria in their environment. Only later was this shown to be DNA and an example of transformation. The whole point of the Avery-macleod et al experiments was to determine what the 'transforming principle' actually was, since some still believed it was protein. I think it's incorrect to say his exp "showed" they get DNA.

https://www.khanacademy.org/science/biology/dna-as-the-genetic-material/dna-discovery-and-structure/a/classic-experiments-dna-as-the-genetic-material