The first time I heard about carbolic acid was in "A Tree Grows in Brooklyn" where (IIRC) it was used for cleaning. It seems to be some strong stuff.
Maybe I miss the point of the original accusation, but purchasing carbolic acid does not seem to me to be necessarily "wrong" in any way. And the fact that Padre Pio died with no scars on his hands seems to argue strongly against a lifetime of carbolic acid abuse.
I just think the whole thing is a weak attempt at character assassination.
I suspect the point of the original accusation is that he could have been applying it to his hands, creating the burns that would then be considered stigmata. Purchasing it and swearing the seller to secrecy suggests this. But, the lack of burns or scars at death suggests against this.