Absolutely does look like an older Sarouk. How old, I don't quite know, but it certainly does show a little wear down to the knot heads, and blooming of the pile.
The thing is, over the years of having a rug like this, you can expect normal wear and tear, but you also have to consider the larger picture. Are there dry rot areas, does the rug have odor, are there any serious stains, does the rug have color run, is there any significant moth damage, etc.
I would have to see a photograph of the entire face of the rug as well as a detail corner shot of the reverse of the rug showing both fringe and knots with a quater on top. This is pretty much the only way I could assist with your assesment of the potential 1K purchase. Size would also help, as well as knot count (Arak's for example tend to look identical to sarouks, however are coarser in knot count, and far less valuable. As I'm sure you know, there are many, many things to consider. This rug looks like it's probably from the mid 50-60s going by these photos, however could be even older. Close ups will help
You also brought up an excellent point in regards to the painting. With a rug like this, you would have to actually ask the seller or inspect it yourself. I say this because the rug does not appear to be painted, however within the last dozen or so years, there has been a trend to remove the pigment from the older, painted Sarouks. However, one serious problem with this is while it virtually eliminates signs of the rug having been painted, it is quite a rigerous process which can take a toll on the rug and the wool fibers as well. As the seller if it had been treated to have the paint removed. One way to ascertain this is how long they've had the rug for. If it is in their house, and they say it was from their great, great grandfather... Don't believe them. :) If they have a bunch of other rugs for sale, be cautious, they could just be flipping. Use your good judgment. It is a very nice classic Sarouk design rug... Great point on the Painting too