Wild Peruvian Amaranth in Eastern Washington

Good Wednesday to you all! I am here to see if anyone knows whether wild Peruvian amaranth could be a harmful plant to introduce in Eastern Washington. I have been helping in my local community garden, and about a fourth of the space was planted with the grain this year. We've been tearing it down and putting it in a pile. I am harvesting what I can and planning to burn the remainder of material. It produces many seeds and has a large root. I am worried it will spread and invade the area, and we are located in the middle of a lot of grain fields. I've included some pictures to verify if it is actually amaranth.

Hopefully others can offer a more definitive answer regarding a 'wild' Peruvian grain amaranth species, but the black seeds, small seed size and large, vigorous plant suggests 'Pigweed' (Amaranthus retroflexus) to me.  If it is a wild grain amaranth, it may hybridize with pigweed, but I doubt it would be as competitive as endogenous, locally-adapted pigweed.  Let's see what additional comments follow.