The summary would be that there is a larger variety of flour (measured by gluten content) in the US than in Europe.
SAJ14SAJ described the gluten categories of American flour, although exact figures for the category limits are hard to pin down. Peter Reinhart says
cake flour has 6 to 7 percent gluten, pastry flour has 7.5 to 9.5 percent gluten, all-purpose flour has 9.5 to 11.5 percent gluten, and high-gluten flour has 13.5 to (rare but possible) 16 percent gluten.
(From The bread baker's apprentice, section Types of flour). I measure exactly my gluten percentages and can confirm that these are good for recipes of the respective categories.
These flours are all made from the same flour grade, with about 50% of the grain removed and only the soft center used for fine bread. The difference comes from the grain type used, hard spring wheat (high in gluten) or soft winter wheat (low in gluten). In Europe, where only soft winter wheat is grown, all the flour is in the 9-11% range. But mills will sometimes enrich certain types of flour with added gluten, or by blending with imported flour, or by milling more of the bran (wholer flour always has more protein) in order to make some specialized high-gluten flours, e.g. Italian pizza flour. These flours are, aside from whole wheat flour, not widely available to home bakers.
I can well imagine that a European trying to bake a European recipe with American bread flour will get bad results. But if they get the AP flour, there will be no problem in the gluten.
There are many other properties of flour which differ, beyond the gluten content. But recipes are never so sensitive to them that they'd fail. If you can't tell the difference between two brands of flour in your home country, then you won't be able to tell the difference between flour with the same gluten content from the other continent either, if both are unbleached and of the same grade (= amount of bran included and particle size).
All in all, this claim sounds like an unfounded emotionally-loaded attack. It is possible that the person who made it indeed failed because of gluten content, because they didn't know that they should be buying AP and not bread flour. Or that it failed for another reason and they were looking for a scapegoat, and garbled some half-remembered knowledge (by the way, while the American wheat is genetically different, the gluten level difference was achieved centuries ago by selective breeding) to excuse their failure.