It is actually possible to set privacy settings in a way so that others can’t see your “Add Friend” button. So if others set the profile that way, you won’t be able to add them. In addition, you are only able to send a friend request once, unless it gets rejected. Friend request should only be sent to someone you personally know for security reasons.
If you feel a friend request is unwelcomed, you could block them from sending a friend request. You can still add them afterwards if you decide to unblock them. The friend you know personally could have blocked you or leaving it pending for as long as she wants. It is better to know a person closer before adding them anyway. Having little true friends is better than having many acquaintances.