If someone put up a sign in a store that said "Burn this store down!" the person who put the sign up is not responsible if someone follows the instructions written on it, are they?

prompt injection is more close to an exploit. a sequence of input that leads to unexpected behavior, exploited to perform malicious behavior.

many exploits are hosted on websites. called exploit kits even. i think prompt injection match such classification. its very similar. a piece of data on the site's side exploits a program or interface on client side.