There is a fairly simple way to test if a fly-rod or blank twists under a relatively low load. Fix the butt so the rod is suspended horizontal, stick a small weight of bluetac on the tip, pull the tip down a few inches and let go. I've used this pretty simple setup to look at the natural and loaded frequency of rods - it's used for the CCF test.
Ideally the tip should track straight up and down. As the oscillation decays the up and down should just get shorter - frequency stays the same (pretty much.) Thing is, typically (arguably more with cheaper rods) the tip doesn't track up and down it travels in an oval - for modern rods the oval path is slight but it's there. I have one nasty rod - the tip pretty soon travels in a circle. Casting that rod - it feels mushy - hard to get a clean loop - there is a slight tendency for loops to come off the tip at an angle even when the rod is as vertical as I can get it. (Some time since I bothered casting with it - I tested it after I tried casting and found it rather unpleasant.)
This stuff has to do with the 'spine effect' and the angle of the rings to the spine. It could also be about the spines on each section of a rod and how aligned those are. The rod builders here can say more about spines than me but it seems to me that the 'spine effect' is less pronounced on the rods I handle now that the carbon rod from 20 or more years back. Manufacturers seem to have built that in - so now a lot of factory fly rods are built to look as straight as possible, and the build ignores the preferred plane(s) of bending which custom builders seem more concerned about? (eg Sage build for straightness, Loomis spine their rods so the sometimes look a bit curved.)
Another point, typical modern fly rod have a fast action, soft tip stiff butt. Older designs including a lot of cane designs, the action was slower, under load the rod bend is more round - stiffer tip, softer butt. I wonder if spine effects are more significant when the action of the rod is slower/deeper.
Personally, some fly rods do seem to track 'true' better than others. However, in my opinion tracking is down to the caster far far more than the fly rod.
Magnus
(PS Will - test a rod you like - find the tip tracks oddly - then cast it. I bet the knowledge that your rod behaves a bit odd in a test will colour how you perceive and cast that rod for some time.)