Science has gaps because scientist do not know things. Non-scientist going "based on what happened to my cousin, this must have been what happened" is not going to fill the gaps in knowledge.
For example, we might now have the 'scientific knowledge' to explain why a particular mushroom is poisonous, but it probably started with a 'avoid it because your cousin died eating that one', followed by the observation that this happened to multiple cousins, followed by some kind of proto-scientific experimentation. None of this might qualify as 'scientists' doing 'science' by our standards, but it's still knowledge.
That doesn't necessarily mean homeopathy should be taken seriously at this point though.
