I have a 2007 LeMond Buenos Aires Triomphe frame, and I have just discovered that the rear tire is so close to the frame that it has in the past rubbed up top. Today, I did my first wheel spoke tune-up and I apparently deviated the wheel from the center so that now the tire rubs on one side. I plan to reset the position of the tire but I am considering going to the original tire size (700x23) from the one that is mounted now (700x25). My question: Are 700x23 tires smaller in cross-section than 700x25 tires? Is it unusual that a rear tire spins so close to the frame? or, am is it OK as long as there is any clearance, no matter how small?
Thanks.

Charles Pappa