In some respects, I would agree, but in shooting these rifles, the classic English bolt action generally handles much better than an American classic rifle. American makers (G&H particularly) tended to make their guns heavier than the English. I think the same holds true with shotguns as well.
As for the modern makers, notice how many now build rifles to what is traditionally the English style? I don't see too many built up with a tight grip, big cheekpiece and heavy forend like the G&H rifles of the past.
One thing I do agree with is that for your money, you do get a better fit and finish from an American custom gunmaker than you will from an English maker.