That is an interesting question, when in an impeachment against the President, the Chief Justice of the Supreme Court is the presiding judge and federal procedure and federal rules of evidence are approved by acts of Congress. The Federal Rules of Evidence are certainly binding on the presiding judge.
You are correct as it pertains to the trial in the Senate, but the Dems don’t care about that. They want him impeached by the House which is not limited by future rulings by the Chief Justice during the trial. They just need to have enough “dirt” so that they can get the Rinos to agree to impeach. They likely want to do this just prior to the November elections in hopes to get enough Conservatives to vote for the Dems or stay home, (Judge Moore is a prime example).