No, it is not true that in all states that if you are convicted of speeding 9 or less mph over the speed limit you will not be assessed points.
Each state has their own laws regarding moving violations and then many states, but not all, have points schedules so that if you are convicted of offense you were cited for points (along with the conviction) will be placed on your driving record.
There are some states that do not assess points if your rate of speed was below a certain mile per hour over the limit or a percentage of the posted limit. For example:
In Ohio the BMV has a different points system depending upon if the citation for speeding was given in an area where the speed limit was below 55 mph or over 55 mph. If the speed limit was below 55 mph then 0 points are assigned for 1-5 over the limit and 2 points for 6-10 over. If the ticket was written in an area where the speed limit was 55 mph or more then it is 0 points for both 1 -5 over and 6 – 10 over the posted limit.
Georgia's violation points list does not mention points for speeding citations of under 14 mph either so it would appear that a speeding ticket for 14 or below would not get points placed on a driver's motor vehicle record.
Oklahoma Department of Public Safety notes that they do not report or assess points to a person's driving record for a conviction of exceeding the speed limit by at least one (1) mile per hour but not more than ten (10) miles per hour.
In Texas the Department of Public Safety notes that points are not assigned for speeding violation that are less than 10% over the speed limit.
Many states do assign points for speeding violations that are 9 mph or less over the posted speed limit. See below for several examples.
The Michigan violation points list states that it is 2 points for a ticket of speeding 10 mph or less over the legal speed limit.
In New York DMV notes specifically that a conviction for speeding 1 – 10 mph over the speed limit is 3 points.
In Delaware speeding 1 to 9 miles per hour over the posted speed is 2 points.
In Pennsylvania it is 2 points for 6 to 10 mph over the speed limit. No points are listed though for a speeding ticket that is only 1 to 5 mph over the posted limit.
According to the Virginia Department of Vehicles violation schedule speeding 1-9 mph above the posted speed limit is 3 points and the conviction remains on your driving record for 5 years.
The Nebraska Point System notes that points are assessed for speeding on the basis of miles per hour [MPH] over the posted speed limit and the type of road. In NE Business and Residential District speeding tickets for speeding 1 thru 5 MPH over the limit is 1 point and over 5 thru 10 MPH is 2 points.
On Nebraska Country Roads / State Highways and Interstates the points system is 1 thru 10 MPH over the limit is 1 point. For 2 points to be assigned one must be convicted for speeding 10 thru 15 MPH over the limit. In this state upon conviction of a violation, points are assessed to a driving record as of the date of violation.
To find out about various states' moving violations points schedules contact their Department of Motor Vehicles or like state agency. They can advise you how many points are assessed, if any, for speeding tickets for 9 mph or less over the posted limit.