If someone makes a claim that unicorns exist, then the burden is on *them* to prove their claim.  The person hearing that claim is under no obligation to investigate it, unless they're interested in the subject.  

The fact that no one else, in the history of mankind, has produced a real unicorn, is also worth considering.  

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.