Vehicle Speed Sensor effect on tuning

In this month's Hot Rod magazine, there is a "rescue" of a 97ish Dodge Ram where they say the vehicle speed sensor was making the engine go lean. Reason being, the truck had larger tires so the sensor was reading incorrectly.

Does this really change the fuel mixture? I've got mine hooked up but have not looked into whether the gear is correct for my tire size. I'm also running a manual trans, so not sure if that also effects it.