Gee, what does it tell us when a single ring or series of rings is wider on one side of the tree than on the other?
Basically that the tree was lopsided. But that doesn't change anything about the validity of the isotope ratio temperature data. In your postulated case, one would take measurements in the wide and narrow areas and compare them.
It tells you the tree was leaning. The ratios of width ring-to-ring are still the same on each side. Wider rings are the same percentage wider than narrower rings.