I agree with this. The problem is, I have yet to see the actual rule adopted by THIS senate saying that a tie fails.
In 1867, CJ Chase did break ties, so there is precedent. In Clinton’s impeachment, they (naturally) ruled that the Republican-appointed Rehnquist could not break ties.
Chad Pergram on Twit has said that’s the case here-—but it’s NOT clear he is citing THIS senate’s rule, and so far, I’m not sure anyone knows what THIS senate’s tiebreaking ruling was.
It was explained that in the senate the VP would break a tie if the majority would benefit by it. If it is not to the majorities liking it is left at a tie and that means the issue fails. It is up to the majority if they want a tie breaker be it Roberts or the VP. The VP does not get a vote in impeachment at all because although president of the senate by title, he is not a senator.
While not a senate rule, I think this is what will happen:
Congressional Research Service: “The Chief Justice, when presiding over an impeachment trial, would not be expected to vote, even in the case of a tie. If a vote on a question results in a tie, the question is decided in the negative.”