Absolutely not.
Consider the following:
Bobby: I ate a ham sandwich for dinner last night. Here is a picture of me eating a ham sandwich. Prove me wrong.
Pete: I don't have to prove you wrong at all.
*Pete walks away.*
This is a completely valid response. Completely. The burden is not then on Pete to prove that Bobby did not eat a ham sandwich for dinner. Pete does not have to rebut Bobby's evidence.
Bobby had the positive claim. The burden of proof is still on Bobby, even if Pete walks away. Pete is completely clean of the matter.
Not if Pete is trying to tell others that I didn’t eat the sandwich.
If Pete just walked away, I could live with his “completely valid response” to not believe me. Heck, I wouldn’t even feel compelled to provide proof or demand he prove me wrong if he didn’t believe me. I don’t care.
But that’s not the analogy.
I ate a sandwich.
Pete doesn’t believe me. Fine.
But Pete’s not walking away. Pete’s calling me a liar.
So I show Pete the photo of me eating.
He says I faked it.
I’m still okay with that, as long as he keeps it to himself.
But he’s not. He’s telling anyone who will listen that I’m a liar.
And a faker.
Those are positive claims. (Positive in the sense of claims, not qualitative.)
I showed Pete the evidence, and if he intends on claiming the evidence is invalid, he is not inoculated from backing up that charge with but a handwave.
You’re free to be unconvinced for any whimsical reason whatsoever. But you can’t campaign in refutation without defending your refutation and then hide behind “burden of proof”. Calling evidence fake is a claim that demands proof, as much as the claim does for which the evidence is presented.