lets say I have a set of data and I want to get a trend line. Why does the fitting accuracy differ so blatantly if the xy data axes are swapped. 
It is the same data, but data for the x axis is plotted as y axis for the opposite figure and vice versa, a quadratic trend line is obtained, but one simply fits far better than the other. Why?
Thanks for your time
They are two possible causes for difference :
FIRST : The two fitted functions (which seems on the same kind) are not really the same.
On the first graph : $\quad y(x)=ax^2+bx+c$
On the second graph the same function would be $\quad x(y)=ay^2+by+c\quad$ or equivalently $ y(x)=\frac{-b\pm\sqrt{b^2-4a(c-x)}}{2a}$. This is not the chosen function $y(x)=ax^2+bx+c$. The axes are swapped but the function is not swapped (which means inverted).
Two different functions means two different results of fitting.
SECOND : Even if the two functions were on the same kind, don't be surprised to get different results for different criteria of fitting. For each chosen criteria of fitting the result of fitting is slightly different. Since you don't say what criteria of fitting is chosen for your two cases, one cannot definitively answer to the question.
Probably the implicit criteria of fitting implemented in your regression software is LMSE wrt the errors on the vertical scale. They are different in both cases since the scales horizontal and vertical are swapped.
You can intuitively understand in comparing with the simplified case of linear regression : On the next figure, for the point $k$ for example, the respective errors $\big(ax_k+b-y_k\big)$ and $\big(x_k-(y_k-b)/a\big)$ are obviously different.
Note : The figure is copied from https://fr.scribd.com/doc/14819165/Regressions-coniques-quadriques-circulaire-spherique Section 3 , page 7.