close, but not entirely accurate.
the mechanical grip a tire has on tarmac(its traction, static friction) is not dependant on tire width, but the compound of the tire, the temperature of the two frictional surfaces(rubber and asphalt), the weight on the tire and that is it. if we have an effective contact patch of 1 square inch with 700 lbs of weight on it, it will have the same traction as 2 square inches of contact patch with that weight on it. why? because now the frictional surface is doubled, yet the weight pushing on the surface is cut in half. however, switching to a stickier tire(and most performance rubbers are) will usually yield better traction obviously, and mostly ppl upgrade when it comes to tires, so they feel more available traction from these upgrades.
threfore, decreasing pressure in an attempt to change the contact patch on the tire on the road is not an effective way of changing grip for more or less under/oversteer.
additionally, if a tire is wider, it might not offer any greater traction to a tire of the same compound and design, but narrower dimensions, but in the dry it WILL however offer a contact patch with a larger face. this allows the contact patch to be more consistent and stable in its traction, as now an uneventy or the like will disturn the larger contact patch less as it would with a smaller contact patch.
So if you want better steering you should adjust your suspension and not your tires