I too have noticed the pledge paddle, but Craig T. Nelson is not a Beta as far as a I can find.
I've never heard of him as being a member, nor is his name on the list of
Famous Betas. A check of our membership directory shows that there was a Beta named Craig Nelson who graduated from Arizona in 1969 but the actor was born in Spokane Washington and I have no verification that he went to Arizona.
Since he is a fairly well known actor, I'm sure that if he was a Beta our GF would be aware of his membership and since nothing from them seems to say that he is, I don't think that he is a member of Beta Theta Pi.