I hope I am not too late for the discussion to throw my two cents in here:
I think process, ingredients, water and fermentation play an equal role. It is a combination of variables and no one thing. While we have documentation of historical and current water profiles, German's cut their water with RO/DI too. I know the Hofbrauhaus in Newport, KY uses a water softener on all of their brewing water. I have found, myself, that when I cut my tap water 50% or 75% with RO/DI I get a different beer. Generally, I prefer the lower hardness water as the malts flavors are richer and bitterness less harsh.
There is much discussion about decoction mashing. I have found it results in a dryer finish (due to the higher fermentability of the wort), maltier profile and more authentic taste. I have been amazed at how much malt flavor and complexity I can get out of a Pils only recipe using a decoction mash. However, I believe the effects of the decoction mash are minimized if you use kilned specialty malts. The melanoidins are already present in the higher kilned malts, so you don't notice the effect of the decoction like you do with Pils only beers.
I also believe the source of the malt makes a big difference. I have made many pils only beers using different cultivars and maltsters, and they all taste different. They all have that signature Pils sweetness, but side by side you can definitely tell they are not the same malt. Some continental pils have too much sweetness and throw off the malt profile, for me; the resulting beers are a little less authentically German. They come out more like French Pilsners, with almost a grape-like pils sweetness.
Yeast makes beer, right, so no doubt yeast makes a big difference. I would even claim that using a yeast outside of its sweet spot even results in a profile that just makes you teeter on the edge and say its just a little off from authentically German. I think in our haste, too warm of a diacetyl rest, too soon in the process, can slightly affect the melding (oxidation, conversion and reabsorption) of flavors. I feel I get a slightly maltier beer when I leave it at 50F for 4-8 weeks, rather than fermenting 2-3 weeks and doing a D-rest warm. I also lose that slight, fleeting, initial sulfur character that I taste in a lot of the great German lagers when I do the warm D-rest. This may just be due to physics and vapor pressures and such when performing a warm D-rest rather than fermenting cold continuously. In terms of fermenting, I think of it like low and slow in barbecuing. Yeah, you can cut an hour off your day by searing, then going low and slow, but it just isn't quite the same as slowly and continuously letting the juices leak out of your grillables and sear over a long period at low temperatures. The hard way is usually the best way, for me.
Then again, what is authentically German anyways. Traditional? Modern? Modern lagers are changing due to economics. If chasing the flavors of a modern, mass-produces German lager is authentic, then I don't want to be authentic anyways.