CAT scales are rarely ever inaccurate. Read their guarantee on the ticket. It is cheaper for them to calibrate the scale regularly than to have to be stuck honoring their guarantee.
The current tires on the truck may be rated for 3750 each, but you have to remember that the Ford wheels are only rated to 3500 each. The wheel is weakest link by which the maximum RAWR on a SRW F350 is calculated. Tires are definitely a concern, but even if you could get a higher rated tire, your wheels would still be a problem.