its a situation that is fictional and terefore unproveable, but the game called sheik a man. And you asserted that Zelda did NOT change sex. I have no more burden of proof than you unless you retract your assertion and change your viewpoint to uncertainty.
An assertion that something does not exist is logically (and mathematically) equivalent to no assertion at all, and disproving that assertion is mathematically equivalent to making an existential assertion.
That is because non-existence is the standing null hypothesis, and an assertion to that effect is a mere reiteration of the null hypothesis, not an assertion in and of itself.
So, in a nutshell, the requirements to prove an assertion apply only to existential statements.
This is all discrete mathmatics, so... an illustration.
if I say: for all n, n^2=/= n*2, isn't it logically equivalent to saying not(there exists an n, where n^2=n*2). And isn't that the same as saying that an existential statement is false when put into plain English? The statement of course is, "there exists an n, where n^2 = n*2".
So, an assertion that something didn't happen or does not exist is disagreeing with an existential statement, and therefore, logically disagreeing with that statement is an existential statement and carries the burden of proof.
To cover all my bases, to establish why logically existential statements do not hold unless proven, take a look at the statement above.
In order to prove it true, only one example is needed, to prove it false, infinite examples are needed. Therefore it is impossible to prove something false, but it is impossible to build any sort of way of reasoning through the world that requires infinite examples (again, think back to my "disprove my invisible unicorn example), we'd be forced to assume everything exists. So non-existence is the operative null hypothesis, and it's disproven by a counter-example.
And there's basic logic conceptualization in a nutshell, I could go on with extended history of the scientific method, but generally speaking, to find the burden of proof, find the the existential statement, whoever is saying something "exists", or that "something should be done", or "something happened", or anything similar has the burden of proof. The person saying the opposite does not have the burden of proof.
*waits for the TL;DR*
well, when there's no spaces in the name, it's hard to see where the intended separation of words is sometimes.
Fair enough, my tag is "Deus" so I sort of assume everyone gets the separation, but, should probably have it changed at some point.