Yes, Weatherby uses two Turkish mfg's to make their SA and PA shotguns, Armsan is one and ATA Arms is the other.
One of the two is also building shotguns for Beretta and Mossberg (don't remember which at the moment).
I have a new (within the last few months) Weatherby PA model shotgun and the fit, finish, machine work and parts fit (barrel to receiver - ease of install etc) is FAR superior to the 870 Express, 500/535 Mossberg that are currently on the market (I sell guns and assemble a lot of shotguns).
The wood stocked models (at least the Weatherby's) stocks and finish comes pretty close to what you find on the 870 Wingmaster's costing "double".
So I "didn't" hesitate to pick up one of these Turkish built shotguns (it's a 20 gauge pump), it carries nice, fits nice, shoots well and as stated, I found the machine work in particular way better than the "entry level" guns from Remington and Mossberg (which you sometimes have to fight with to initially get them assembled).
(I also own an 870 Rem, an old Winchester Featherweight and an H&R shotgun, so not a singular comparison on my part)
One common complaint with the Turkish guns has been the trigger which can be rather heavy (one article from a noted writer called it "unusable").
I measured mine just at 9 lbs, so yes, heavy, but in the field I didn't "notice" how heavy it was and it hasn't been a hindrance so far. I initially considered having it worked on to lighten it a bit, but have got used to it now and don't find it bad at all.
(not to confuse your decision further)
You also may want to add the Winchester SXP to your list to consider. I will state that I am not a Winchester fan although I own a couple, but my position on them is due to some uber-poor customer service just prior to the company going bankrupt (and I hold a grudge still) - anyhow, they are now owned by FN (Belgium) and their product line seems to be decent. I recently got in an order which included a few SXP Field models (which are price competitive with the 870 Express, 500 Mossberg, PA Weatherby etc) and at least from an assembly, fit/finish etc I find them nicer then the Rems/Mossberg's - no first hand as to how they shoot or function, but they seem to be "starting out" a little better built than some of the other "starter" guns - so maybe worth a look.