Home Depot (the company) will not make any effort to ban me from using their chain even if an employee did make me leave the premises. I could just go home and order it online from HomeDepot.com and have it shipped right to me.
So, much as after you kick someone out of your store they could order on the home depot website, they could also just go to Lowe's and say nothing. Neither company is really to blame in that case. On the other hand, I wouldn't say that you shouldn't escalate to law enforcement if someone is threatening to go lynch someone in your presence.