To "ground fill"or not to "ground fill"?
Sure, lets take the common case of a microstrip.  It's impedance is a combination of itself and  it's return path (and the dielectric but lets keep it simple).  In a microstrip's case this will be the reference plane underneath.  

Now if you go and throw a piece of grounded copper right next to that microstrip, it's impedance is now a combination of itself, it's reference plane and that grounded copper next to it.  You usually can't get a 100% symmetrical fill around the microstrip, because of vias, other lines or just going into a pin on a package.   So in short anywhere you have this copper fill changing your impedance you are going to get discontinuities or changes in impedance.

For example in the image below there'd be a discontinuity for the main trace where the flood is interrupted by a via.

 

To be fair though there is a type of transmission line we sometimes use called a co-planar wave guide which essentially looks like a trace with two wide copper fills along it's sides (symmetrically along it's sides).