what are the odds that modern birds evolved not from theropods, but from small iguanodonts/ornithopods during the early cretaceous period?

also, what are the potential chances of issues in the archeological findings arising due to convergent evolution of traits between omnivorous/carnivorous ornithopods, and the theropods? most notable example being therizinosaurus, an incredibly poorly understood dinosaur.

pic related is Thescelosaurus, an omnivorous ornithopod, and a relative of the hadrosaurs.