As long as you have 3 x 10-gauge wires + ground, you should be OK to put in a 4 prong outlet. The 3 prong outlets were indeed designed to bootleg the ground to the neutral, which was a bad idea. As one website noted
So, why did the NEC make the decision to switch from 3-prong to 4-prong dryer outlets in new homes? Although the old 3-prong outlets were effective at providing power to dryers, they had one major flaw: the ground and neutral wires were grouped together, creating the potential for shock. 3-prong dryer cords contain two ‘hot’ wires along with a third wire that contained both the ground and neutral wire. If a current happened to make its way onto the ground wire, it could travel up to the dryer.
The more recent 4-prong dryer cords feature two hot wires, a neutral wire and a ground wire. This eliminates the possibility for a ground current traveling to the machine, as it features a separate return path for unused power.
The ground wire is always smaller than the hot/neutral because it's not meant to carry a load like the other wires do.