That doesn't really refute any argument about the One Ring also being a Lord. It merely states that Sauron had the title as well which wasn't something I think anyone was refuting. The original title of the book was "The Magic Ring" which could lend weight to the argument of the ring being the Lord referenced. The ring also contained enough of his power that he was left with nothing once it was destroyed. Which again lends weight to the argument that the true Lord of the Ring was the ring itself.
Like I said I don't believe that to be the case myself but it is something that can be made. Unless there is a quote from Tolkien stating such is is more ambiguous then what the two towers references. As he states what he was referencing and what the text indicates is the reference.