As with most generalizations, this one has some basis in truth. Parkland design is common in the U.S. because the main population centers are located in envrionements with fresh water and precipitation, heavier soils, and trees. But if one travels the country, there is quite a bit of variety, and more so today than ever before.
As Philip notes, trees were added after the fact at many sites, but trees (particularly deciduous varieties) have always been dominant in area landscapes. In effect, I think golf courses were adapted to the local environments (Shadow Creek in Vegas being the exception), much like links courses fit the Scottish coast.
I would suggest that this adaptation to the local climate and soil conditions in the U.S. is not much different. Considerable wind, lack of rain or very porous soils result in wide fairways and firm conditions. While many prefer these conditions, "American Style" golf is better than no golf at all. I am curious, are London area courses when compared to, say, NYC or Chicago courses by age that much different?