Was looking for this for the past few days.
Here's my example with print screens.
It looks like the traces are first drawn from pad to pad (copper around the hole). Which is good at 24mil thickness.
If you make an adjustment in width, the trace line is enlarged around what is already there, without correcting for length, hence covering the holes partially. This isn't the problem for me; on the contrary:
When you quit Fritzing and reopen, all the traces are redrawn from pad to pad (not covering the holes). If you reduce width at this point, it will lose contact with the copper altogether.
So my issue is that all the widened traces become less in contact with the pads, like you mentioned.
I think the solution here would be to adjust the "roundness" of the trace ends, instead of making them a half-circle they could be rectangular with rounded edges.