I don't know why Mathcad does not return an error message when you try to do a surface plot with simple point data but it doesn't. Instead it tries to create a surface by some sort of interpolation.
Because you can plot a surface using x, y, and z vectors. As you say, it uses some form of interpolation, which does not always work so well even if the data is on an evenly spaced grid. The plot is more reliable if the x, y, z vectors are converted to X, Y, Z matrices.
Unfortunately Mathcad does not provide any 3D surface fitting or regression methods, so unless you are able to rearrange your data to form a mesh you will have to program that kind of routines on your own.
You also search this forum for buzzwords like "surface fit" - maybe someone had already posted a routine you could use.
Fitting a surface to 3D data is simple enough using minerr, but this data does not look like a surface that could be fitted with a function with any reasonable number of parameters.