Yes - I believe this is true.
The positions of the Great Circles are not fixed. Their exact locations are relative to the Earth's axial tilt (obliquity). The axial tilt fluctuates within a margin of about 2° over a 40,000 year period. If it weren't for the Moon, this degree of fluctuation would be even greater. I've seen latitude values from different Epochs, but not on a yearly basis although I'm sure it exists. That said, I think we're talking about tenths, hundredths, or thousandths of a degree difference so it's not a radical movement.