I would say that is incorrect. Maybe that's what's been communicated towards the public, but IMO that is not the real reason.
First of all, I wouldn't say the Impeachment Process (neither House, nor Senate) is a Trial in the Sense of Rule of Law. They are (essentially) votes in the 2 legislative chambers. That is not a Court of Law.
And that in mind, I don't think the Reps and Senators really voted on evidence or any argument presented (whether right, or wrong). They voted on what served their political angenda. And I think not making Al Gore President (at the time a likley candidate for the 2000 Election) and potentially giving him a boost this way - is the more important reason in Clinton being aquitted. The Republicans didn't want Gore to take over. It's as simple as that. IMHO.