Adam:
Don, not Dan, has a pretty good handle on this.
As Don says, selecting the turf is certainly important, but I think less dependent on how, or with what materials, the green is constructed. The bigger decision comes back to COST, the architects input (hopefully the owner listens to his/her experence in this area), as they together give thought to; performance expectations and/or requirements, and by that I mean the internal drainage properties of the green profile, the maintenance expectations desired by the owner and techniques available to the super to manage the greens in the long term, the specific site conditions, design intent by the architect, the intended constructiion methodology/approach, the equipment to be used....
As you can see, there are many factors and each with variables which translate into pros and cons of green construction. In the end, the architect, the owner and the super must decide what is the best approach/technique to use given the set of parameters and costs restrictions, if any, that exist, to build the best they can for the money. With this in mind, however, each owner should be informed by either their architect or other experienced and knowledgable advisors about the long term costs involved with their decision to build one way or another since each one can have significant consequences on the final outcome and the potential nightmares the owner and the super will face for years to come.
Sure the construction materials "support" the grass, odd way of saying it though, however, the ability of some materials, when mixed together, along with their own internal properties can be better or can be compromised for the need at hand. I'm not going to get into a real technical discussion, but, water (rain or irrigation) moves through the soil, depending on the engineering properties of any given soil material used, the water will move faster or slower. During that time period, water is available to the grass plants for their needs. If the water stays in the green profile too long it can stunt the growth ability of the grass, hey my feet are too wet and I'm getting cold could you please drain away! There are many other problems which can result from the green profile being too wet, but you get my point. Naturally then, if the soil profile in the green has properties that cause it to compact together too much, the water can't get through the pore spaces and therefore it can't reach down to the grass roots.
There is a balance of soil compactability, enough pore space, internal drainage characteristics which are directly related to pore space and the proportioning thereof, all of which lead to the ability of air and water, which by the way is carrying nutrients, to reach the roots. Applying ferts are fine, but worthless if the soil doesn't have the properties to allow the nutrients to penetrate.
Whew! I have said way too much and likely pissed off some superintendent somewhere, so if I have I apologise, but Adam I hope this finally puts your mind at ease.
Good god, I was starting to get dizzy there for a minute...I wonder if this is how Tom Paul gets at times!