Frying with butter - toxic/unhealthy?

Sometimes I use butter instead of oil to fry scrambled eggs or potatoes.

I've heard that it's unhealthy when butter melt alone on the pan (before you add something). Is that true?

If so, is it still unhealthy when butter melt with eggs already on the pan? I mean, it's impossible not to have completely melted butter and fried eggs, potatoes etc.