Burden of Proof
In philosophy (It is also a specific legal term) the requirement to justify a claim, or the 'burden of proof', is always on the claimant, especially when it challenges a perceived status quo.. If Janet proposes that vaccines cause autism, it is up to her to provide good evidence of that claim. John, on the other hand, says that he has seen no evidence for that proposal, therefore he is reasonable in rejecting it. Similarly, if John claimed that acupuncture can cure migraines, then Janet, who has not seen sufficient evidence of that, is also reasonable in rejecting his claim.
Notice that in rejecting these claims, neither Janet nor John is proposing that Vaccines DO NOT cause autism, nor acupuncture CANNOT cure migraines, merely that neither has been presented with sufficient evidence for the positive claim The null-hypothesis would then posit that the negative - or skeptical - position was the reasonable one. Often proponents of a claim will try to shift the burden of proof back onto the other person; Janet may say: "Well, you can't prove vaccines don't cause autism" to justify her claim, putting John in a position were he feels compelled to present his evidence to the contrary. Of course, he does not need to do so. By demanding evidence that vaccines don't cause autism, Janet is committing an 'Argument from ignorance' fallacy; saying something is assumed to be true because it has not yet been proved false. It is up to Janet to present her evidence and only if it is sufficient to warrant her claim that vaccines cause autism, is John being unreasonable.
Of course, these are abstract philosophical concepts and the real world is much more messy. We often feel pressure to justify a contrary stance and in doing so accept the burden unnecessarily - there is lots of evidence that vaccines don't cause autism and acupuncture cannot cure migraines - however there are good reasons to remember that when someone presents you with a claim about something you don't know much about or you think is likely unknowable, let the claimant make their claim and present you with sufficient evidence. If that evidence does not meet a good evidentiary standard, you do not have to justify the contrary position. It is up to them to meet that standard and until then you should remain skeptical.