Yes. The law does require all drivers to drive within the posted speed limit. In most cases these posted speed limits apply and if you're driving within that posted speed limit, you are driving within the law. However, there is another law which provides that regardless of the posted speed limit, you are required to drive at a speed which is safe and reasonable in light of the existing conditions at the time and place you are driving.
For instance, if there is hazardous snow on the ground you are not free to drive 65 miles per hour on a highway if driving at such speed causes you to lose control.
Another example is if you are driving in dense fog. Regardless of the posted speed limit, you must slow your vehicle down so that you are driving safely in the fog. This may mean that you are required to drive no more than 5 or 10 miles per hour.
This rule which requires all drivers to drive at a safe rate of speed in light of existing conditions is simply a common sense rule which is consistent with the law that requires all drivers to drive their vehicles as a reasonable and prudent person.
This reasonable and prudent person test applies regardless of the posted speed limit.
We all have a duty to drive our vehicles in a safe manner. If we disobey the law and do not drive safely and if someone is injured as result of that unsafe driving, we are held liable for all damages which result.