Truth really doesn't care about where the burden of proof lies. The ability of someone to present evidence or argue a case doesn't affect whether the proposition they propose is true or not. A real truth-seeker is looking for the truth regardless of where the burden of proof lies (though of course, that's not always easy).

So when someone makes the unicorn claim, the correct response is "prove it," and if they can't, then the null hypothesis is the only rational one.
Any other approach means we have to accept that leprechauns, Santa, The Easter Bunny, Thor and Zeus are real, which makes no sense at all.

You don't have the accept that leprechauns are real; that's kind of the point. Obviously being skeptical doesn't mean that we accept things without any proof. The point of the article was that, you can entertain things without accepting them, and you can consider the probability of the reality of a proposition to be likely or unlikely, without fully accepting or rejecting it.

Have a good one