I don't think this is a valid suggestion, but, I can at least guess at the reason.
I think the motivation is wanting to make sure that you can erase all trace of the password in memory promptly and with certainty after it is used. With a char[] you could overwrite each element of the array with a blank or something for sure. You can't edit the internal value of a String that way.
But that alone isn't a good answer; why not just make sure a reference to the char[] or String doesn't escape? Then there's no security issue. But the thing is that String objects can be intern()ed in theory and kept alive inside the constant pool. I suppose using char[] forbids this possibility.