Not all roots are starchy, eg: onions, garlic, carrots, beetroots.
Although onions and garlic do contain inulin, and I had to introduce that slowly and acclimatise my body to them, after which I had absolutely no issue with those two roots.
All plants have tiny amounts of starch inside their cell walls, but that is nothing to worry about any more than the starch that animals produce in their livers.
The iodine test isn't really good for telling you how *much* starch is present. Just that there is some.