The question is not about who ordered his tickets or who made his hotel reservation or who paid his travel voucher. The question is about whether anyone in the White House knew about Wilson's report before purposely ignoring his "facts" and sexing up the State of the Union address with those 16 words. That's why Wilson claims the Office of the Vice President knew of his trip and his trip was to answer whether those words were correct or not as least in his view. Wilson clearly believes that the Office of the VP initiated the chain of events that led to his trip and by inference it received his oral report afterward debunking any Niger sales of uranium to Iraq. When intelligence analysts got Wilson's report they thought it supported the contention that Iraq sought to purchase uranium from Niger. Whether or not that was briefed directly to Cheney we do not know, but Wilson believes he debunked any memo purporting to show Iraq actually purchased uranium in Niger. He thinks he was selected at the CIA to answer that question and he did so, but was purposely ignored at the White House so they could sex up the SOTU address. He's wrong.
The question isn't whether he is wrong about things he doesn't know one way or the other (i.e. the VP being briefed on his visit). The question is whether he lied - as charged. Nothing in your post points to a lie.