Yes. New users with 1 rep can edit their own question.
I suspect the phenomenom you noticed is mainly caused by:
- The fact that people are more used to forums, where the preferred way is to add a new post to the conversation instead of editing the initial post,
- Maybe to a less extent that the "add a comment" link may be more visible than the edit one.
A user can always edit their own posts without any reputation prerequisite (this concerns both questions and answers without time limitation and comment during a few minutes only). Do not hesitate to encourage them to use the "edit" link instead of adding new comments. The first edit will even be awarded by the "Editor" badge :).
Moreover any user can also propose edits to any posts, however while their reputation is below 2000 their edit proposal will need to be reviewed before becoming active.