Science advances in strange ways sometimes. Plate tectonics started basically with the anecdote of "south america really looks a lot like it fits into east Africa", but wasn't believed at first due to no hard data.

Anedoctes are not data, but when you have some with no data, instead of ignoring it you should take it as a signal to go search if there is data to support it. Great scientists and mathematicians usually have good intuition of things to research, not because they have data, but their mental models of the subject tell them that there should be interesting data there.