Actually, you will find that some slitting saws and arbors have fairly low run out. I use Martindale slitting saws when I can and those are pretty flat. Keo and Robbjack make good ones but they're expensive.
I found that the arbor is really important. It has to be accurately made and to fairly tight tolerances. Sierra American makes really good ones. Those multi-step imports are not worth buying, IMHO. If you make your own, the OD of the arbor needs to be about double the hole size of the saw. For example, an arbor for a 1/2" hole saw will be about 1" OD. The arbor diameter should be somewhere near 0.0005" smaller than the nominal size of the saw hole and the face cuts on the arbor and washer need to be very clean and flat.
Saws will have their own run out and I think this has to do with heat treating a very thin piece of metal that have been worked on the rim. It's surprising they don't warp more than they do but good saws from good makers are pretty accurate, I think.