It's a shame they didn't even suspect Jeanette who was right there when he coughed out blood. Oh gee I wonder how the news could've gotten out. Sure it wasn't actually her, but from their perspective, she should have been a suspect.
Besides. She DID tell a guest in her home that the King was...
Innocence and naivety is NOT an excuse when it results in the loss of life. Not when it hurts someone physically or emotionally. It doesn't excuse the damage one does to the other.
People people. Unlike other reincarnation stories, this chick's past life was spent in a room. She literally learnt nothing, experienced nothing. She didn't have any lessons, didn't socialize, she's pretty much a blank slate anyways
She is not consistent at all. Zero survival instinct too. If she never wants to be recognized as a Saint. Don't use her magical powers. At all. Simple as that. No risk that way. Geez