I think that what actually happened here was:
> You have a 64-bit fedora OS (x86_64)
> You ordered YUM to install 32-bit qt and qt-devel
> YUM, not being the sharpest knife in the drawer, attempted to satisfy dependencies (immediately or ultimately: 32-bit libGL.so) by pulling in the most unlikely (in fact: stupidest IMO) packages that supply the dep: xorg-x11-drv-nvidia* from RPMFusion. Only after you specifically excluded those did YUM fall back to the actual, intended target package: mesa-libGL.i586 from the standard repos. We saw this more clearly last night in a couple other threads, with similar issues.