I assume he meant it was not on the same grid as the rest of Manhattan. And not to completely disagree but its difficult to make an analogy to Europe. When you consider that the old core, the historic centers of the cities you mention are each about the size of Manhattan below Canal St, or maybe to be generous, Houston St you can't really compare them to the rest of Manhattan, its apples to Oranges. All those cities, just like NYC, experienced massive exponential growth in the later half of the 19th century with the industrial revolution and the massive urbanization that accompanied it. So if you zoom out and look at those cities and the same scale as the whole island of Manhattan, not just lower NY, you will see a similar pattern.
Take Vienna for example. The area inside the Ringstrasse, the old walls of the city, is centuries old. We'll set aside the Rinstrasse itself for moment since the glacis was left vacant until the 1860s. The area outside of the Ringstrasse is considerably more ordered but still somewhat organic, the 'plan' of much of this area dates from the 17th-18th centuries. But look further still past the Gurtel to the area of the 19th century development where the city was built up out of nothing, not overlain upon old Palace grounds or the small rural suburbs of Vienna but upon empty land, like the aforementioned glacis upon which the Ringstrasse was built. This area is all gridded streets. True its not one single overriding grid like Manhattan but a series of grids that parallel and radiate out from the central core. But Manhattan is not a radial city but grew longitudinally up a relatively straight island. At any rate you can see the same pattern of development in nearly every European city. A vaguely rectangular inner core, the old orthogonal Roman Castrum degraded by time and overlain with medieval constructions, then a warren of true medieval streets stretching to the old walls then a slightly more regular often radial out core from the post-Renaissance time and then the vast sprawl of the 19th century city.
And this should not be surprising in many ways its inevitable. Western urban development has a long history of regularly planned cities. Look at the cities of the Greeks, the gird plan of Miletus for example. Or the Roman Castrum, with the fundamental grid parti of Cardo and Decumanus that forms the core of almost every city in Western Europe. Look too at the medieval expansion of the city of Florence during the time of Arnolfo di Cambrio, the his walls dramatically increased the size of the city and the new area was developed with roughly strait streets, some in parallel some radial. Or look at the Florentine new towns like San Giovanni Val d'Arno or their Venetian equivalents like Castelfranco Veneto. All planned on a grid. Then the great burst of activity in the Renaissance and the Baroque cities like Palmanova, Neuf-Brisach, Saarlouis and Karlsruhe to name a few.
The point is rapid development was almost always done a regular plan or with some overriding strategy. The European city's irregular-ness comes from its long history. Development in fits and starts, construction destruction and reconstruction, expansion followed by contraction. So the old Roman plan crumbled and was built over erratically in Medieval times, the new medieval zone declined during the black death and through war and was slowly rebuilt. Someone's vision is only partially executed and then partially destroyed and then rebuilt. This LONG history is what created the palimpsest of the European urban plan. So in short NYC is simply too young and has grown too fast. You can't have the city 'planned' and developed in less than a century in a way or in a manner that would produce the same result as a process that would normally take centuries. That is the antithesis or organic, it would be a conscious decision to plan a city irregularly. An impulse never before demonstrated in the history of Western urbanism. Probably the best you could have is a moderately more organic grid, perhaps fractured into a series of grids that radiate from Broadway or shift angles slightly on different points on the island. Perhaps a bit more like the other boroughs but almost certainly not like an old European city writ large, multiplied 7 or 8 times over across the island.