Nonsense.
If by “universities” you mean institutions comparable to the British universities of the time (which themselves, apart from Edinburgh, were well behind the German universities of the time) there were none in America at all! On a rather looser, more inclusive definition, there were a few of what were basically seminaries, of which a handful (Harvard, Princeton,…) might have had decent academic standards, plus maybe a few agricultural and other colleges, probably mostly nearer the academic level of a modern community college than that of what we would consider to be a university now (or what Europe would have considered to be a university then). Some of those colleges may now have evolved into distinguished universities that boast about their early dates of foundation, but they weren’t universities back then, and I very much doubt that, even by the most inclusive criteria, there were anything like a hundred of them. (And, incidentally, applying those sorts of inclusive criteria to Britain in 1835 would certainly net you a lot more institutions of “higher education” in England than just Oxford and Cambridge. Some of them, including several of the Dissenting Academies that flourished in Britain from the mid-seventeenth century onwards, were academically quite distinguished, producing important scientists such as John Dalton, the originator of chemical atomic theory.)
As I pointed out in my post below yours (not then having seen yours), the huge advance, both quantitative and qualitative, of American higher education happened after the Civil War, not really taking off until well over a decade after, and the first “real” American University, i.e., the first research university with a serious provision for graduate education, was Johns Hopkins, founded in 1876. Others soon followed, with older foundations also upgrading themselves. (This, of course, is also, not coincidentally, the period when America’s population really started to grow rapidly, largely through extensive European immigration.)
You are right that there were not many British universities in 1835, and that (apart from the Edinburgh medical school) they were not up to the standards then being set in Germany, but there were not many, if even any, in America before that time, or even forty years later. The expansion and improvement of higher education in Britain got going several decades before it got going in America, and, even up until the first decades of the 20th century, the American professoriat had mostly, of necessity, been educated in Europe (mostly, in Germany, but Britain and other countries contributed too).
It occurs to me that the strong association between American Universities and the distinctively American sports of football and basketball may have something to do with the fact that these sports were also invented in the late 19th century, just the time when American higher education was itself getting going.