incorrect on all accounts

a wider tire does not ALWAYS mean more traction
in a straight line, it does in a way
but when you turn, a wider cheap tire will cause worse handling in a turn, becuase hte sidewall stiffness is lower, thana higher end tire.
so when you turn, you have to wait for the tire to flex as much as it has to, then transfer the car to the turn.(**** i cant explain it better right now)

so no, wider tire is not always better