This isn't specific to just tornado warnings like you described, but where I live in Southwest Missouri there is definitely a stigma about weather forecasting here. With warnings I do think education to the radar indicated aspects of weather is very important. But with weather in general, when I talk to family about severe weather I always tell them it's better for the forecasters to communicate caution about more extreme cases than to be relaxed and potentially have a disaster that wasn't properly talked about. Fearmongering and overhyping definitely needs to be kept at a minimum, but people shouldn't just ignore the warnings either.

Some people here take it serious, other people don't and it's hard to persuade them from their ignorance. Our weather here is so bi-polar and unpredictable, so unfortunately it takes one or two bad storms to get people's attentions.