actually, the scene occurs if you have the item the professor gave you that attracts them (hence why it goes to sting you in the first place). I believe it gives you a skill check to dodge it that requires a particular stat to be a specific level but I can't remember what it was or how high it had to be; I think it was the agility stat?
but if you choose not to dodge, then yeah, you end up in the hospital. you can also trigger the event even after completing the quest simply by retaking the class. and as long as you have the item each time the bug breaks free, it will try to sting you