Nichols was one producer, many of similar ilk have been attributed, and rightly so, to nichols due to the quality, genre, etc.
The rug is clearly hand knotted. Whether or not it is authentic Nichols, I do not know without pics of selvages, etc.
I would not allow the print on the back to indicate this being a true nichols, as almost anyone could have done this. There is an unbelievable extent to how rugs are often passed fo what they are not. We won't get into this now.
However....
I would say grab it, and do so quickly if it's in good shape with even wear no problems other than needing a cleaning. Even if it's a newer reproduction, which I am not convinced that it isn't, you can still flip it for more than the 1200 they ask perhaps more depending on condition. Other ways to identify nichols rug include the selvages, selvage wrap, quality of wool, design execution (nichols type are one of the few rugs during the late first early second quarter that was twisting two diferent color wools to compile yarn ply in one knot to have muti coloring.) and yarn ply being 3+. These are not the only identfiers, personally I think the wool looks a little flat to be an original, but that will have to be determined by someone in person, or specific photographs which would aid identification online.
The wool is almost always a good shiny sheen and unbelievably heavy for Nichols (and even repro). 12x20 you're going to want to bring a friend, a full pile nichols rug is almost always 1+ pound per square foot with full pile, bringing this carpet to a projected weight of 240+.
Do remember, you may have to sit on it for a little while. As with any purchase, if you have any doubt of ownership being theirs, ask the seller to sign in writing that the rug is theirs, and it is within their right to sell it. Just tell them you need a receipt for documentation purposes so you don't freak them out.
I wouldn't negotiate, it seems like a very fair private party price given final identification may mean it's a repro, so there's potential risk on your part as a buyer but you should be ok in the end
