you've just changed the tense there, factor30? I'm not sure this and that are time-sensitive: this thread doesn't become that thread because a day or two have passed. It remains "this thread" because it's the one we're talking about right now.
Hence my suggestion that "I told him we did not have a vase, although this statement [the one I mentioned 0.07 milliseconds ago] was not strictly true" is okay - it's the statement I'm talking about right now, in the very same sentence.
Sorry, uberloitenment, this is all getting more complicated than you probably need.