This is a commonly repeated factoid that seems to come from the 2003 book What Every Person Should Know About War by Chris Hedges. Is it true? When, exactly, was the last year in human history where two governments were not fighting each other?
Isn't this an unanswerable question? For much of that time we don't have any sources on what was going on in the Americas for example. While we could've had one or two years of peace in Europe and Asia (though I doubt it) we don't know what happened in the Americas. Could've been loads of wars.
Hopefully someone will drop by to address that specific claim, but meanwhile, you may be interested in this post from the FAQ