the thickness of a single sheet of drywall
Did they happen to specify how thick that single sheet should be? I bet that they didn't and are being over protective, because they sell drywall in varying thicknesses from 1/8" up to 5/8".
But I don't think they're being TOO over protective, because I think that's the exact same mount I used, and it mounts using lag bolts. Lag bolts are very heavy duty bolts that are driven into the wood and bite into it to create a very strong anchor.
Their strength, however, is in the depth to which they sink in the underlying wood - the deeper they sink the more thread length is biting into the wood holding on tight. So - if you get too shallow of an installation, you don't get the strength you might need.
I read another answer where someone claimed they had a 50" TV mount just in drywall, no studs!
Not for long, I bet...
The other option I considered (although am loathe to attempt) is to cut away the extra drywall, attach some more wood onto the stud (enough to make up why width of the drywall I removed) and attach the mount to that.
You could do that - I thought about doing the same thing - and the way I would do that is to use a multi-tool (below) to cut out the drywall in the same shape as the back plate of the mount, affix that to the studs very securely, mark the stud location on it and drill through the plate into the studs and mount the panel.
HOWEVER - I suspect there's an even simpler solution.
Get longer lags.
They come in a wide assortment of depths and diameters. Just take the lag bolts they supplied with the mount, go to Lowes/Home Depot - and find one that's the same diameter as what they supplied and about 1" longer than what they gave you, and use those instead.
It is possible to fabricate some sort of support no matter what, it's more about what is the most expedient method of support that is not completely ugly. As mentioned by maple_shaft, there would typically be an intermediate stud between the corner and the window. It is conceivable that 24" spacing is being used and the only structure is at the window and at the corner. The window would typically have a least 3" width of rough framing at the side, mostly behind the trim, but allowing for frame thickness and rough-in allowance, there should be a bit of framing behind the wall finish you can nail into right along the edge of the trim. Even if completely behind the trim, you could, for instance, use a 1x6 support and dado it into the trim so that it has positive attachment to the underlying framing.
So now you have two points of support, one either side of the clothes pole. A 1x6 will be adequate to span between these points and look compatible with the trim. I agree you should use a proper clothes pole instead of copper. I assume it is the hard type that is somewhat rigid. (The soft type is obviously unsuitable) Even if it appears sturdy initially, under constant load, it will slowly bend over time (creep deformation) until it pulls out of it's support and falls.
Best Answer
That's not a single stud mount any more than the one you have is--it's just a different design for a different purpose. Use your mount with two or three good lag screws into the center stud and call it a day. 3/8" x 2-1/2" should do, piloted to 1/4" full depth plus half an inch.
If your mount flexes a lot it's crap and you should buy one built to a higher level of quality. The mount I bought 12 years ago weighed twice what most modern ones do, but one bolt would've done the job even with the early, heavy TV we had.