This may be too subtle a difference to what you say above but I think about it the other way round (at least when building native soil greens on sand): Create the green complex and surrounds as one and then make sure the final mowing line of the green surface doesn’t just follow the top of the pad.... i.e. the surface should fall over the edges and flash up the sides.
Ally, I find this comment very interesting. When thinking through the concept of greens v surrounds, at one level, the distinction comes down simply to the mowing lines. At that level, as you say, just mowing the complex in a way that "surround" topography is given "green" mowing treatment naturally integrates the two.
This goes to a question I've seen posted here a few times: what's the point of tightly mown areas that are too steep to hold a ball?
False fronts are the most common representation of this feature. But if you bust the greens mower off the pad you are probably going to be going down (or maybe up) some terrain that, once cut to green height, won't hold a golf ball at rest.
I think that this is one of the great features of a golf course, and I am always happy to see when a course is presented such that there are "dead zones" like this, around the green, where the ball will not come to rest and where no shot will originate.
This doesn't have to be penal. Punchbowl greens, backboards and sideboards all work on the same principle. We all like to make use of these when we can.
When laid out thoughtfully though, using mowing to tie together the foreground and background of the green while creating "hazards" disguised as the "objective" is a pro-move in my book.