Who still believes this? Maybe when radials first came out i could understand that it was caused by the new technology with limited radial knowledge and a issue with tire construction more so than turning them to soin the other direction. I have rotated tires on my truck every 3k miles for the last 10 years approx 80k miles and always bring the rear straight forward and cross the front to the rear. Never had a issue. It will not hurt to change the spinning direction of the tire so long as they are not directional.
Most tire issues are either improper inflation or aged related. Granted there are some with factory defects. Dont you think if tires were only made to travel in one direction they would all be directional? Not insulting anyone by any means, just my take on the issue, have been installing tires for about 10 years and have never had a issue with rotating them and changing travel direction