OK, count me back in this one.
Jim, it appears you are arguing on both sides. If the odds are 1 in 38 for any number and each spin is an independent event, not depending on the previous spin or depending on the future spin, then the 2nd spin must be 1 in 38, not 1 in 38X 38.

Here is the fly in the ointment. Casinos go to great lengths to keep wheels free of dirt and burrs. Service of wheels is not cheap. One tiny speck can effect the outcome of the spin. A tiny nick can throw the odds way out of kilter. In most cases they go against the house as gamblers watch for these little edges.