A question related to baseball AND "South Pacific"

In "Bloody Mary," a sarcastic song about a native woman, the sailors sing:

Her skin is soft as DiMaggio's glove
Her skin is soft as DiMaggio's glove
Her skin is soft as DiMaggio's glove
Well, ain't that too damn bad?

While I understand that the famous centerfielder's glove was made of leather, aren't well-worn baseball mitts legendarily soft and smooth? And whose glove would have been "weller-worn" than Joltin' Joe's!

So, is this just a case of Hammerstein the lyricist not knowing baseball or is Mary more of a catch that we might think?

Discuss.