Nope.
As others have pointed out, this is not true. When you rotate the whole movement, the date stays right side up if you still display the date on the right-hand side.
Here's a 2836 in the regular orientation
and rotated 180 degrees
As you can see, the dates are still right-side-up on the right side of the movement.
The only way you need a date at 9 datewheel is if you leave the movement the way it is, and have the actual date display on the left side (like on the Tag Aquaracer).
Now, as someone pointed out, the one issue is that the date disc has 31 (an odd number) of dates, so exactly across from the stem position is halfway between two dates. If you just turn the dial around, the dates won't be aligned. You can usually correct for this by modifying the date jumper spring, but with a Rolex rep the even easier solution is to remove and remount the datewheel overlay.