That is correct. The US did not arm Iraq with WMD. The mistake we made was unwittingly send them the germs that they ended up turning into WMD, i.e. anthrax, botulinum toxin, etc.. They would have ended up getting it elsewhere, but it is what it is. We did not arm Iraq with WMD!
The CDC (Center for Disease Control) sent the Iraq Department of Agriculture the anthrax. The USA sends anthrax to a lot of developing countries for live stock research purposes.