We've got a patch of Johnson grass that is fenced off from my horses.
There's a certain time of year when Johnson grass releases cyanide. My eye doctor knows that because they did an autopsy on his cow
This link uses the word "invade" when referencing Johnson Grass.
Johnson Grass Control | Missouri Department of Conservation
I'd bet my last truck load of bermuda hay against what you're looking at that Johnson Grass grew in with the bermuda and they couldn't kill it. The bermuda got so overrun with Johnson grass they decided to market it that way.
My bermuda hay is locally grown and there is about five percent of Johnson grass in some of the stemmier bales. My horses won't touch it - not any of the four of them.
I'm not saying not to buy the hay but here's the information as I am familiar with Johnson Grass, plus a link for you to decide