I generally don't knead, I make turns like one would for croissants. (3-4 at the most) This makes layers, which, most people seem to like. Like Chris says, don't overdo it.
It could be your flour. There's no standard for AP flour in the US, and it varies by mill and by region. Big name flours make their Southern blend more like cake flour because they know more people use the flour for biscuits. The same company's Northern blend will be a higher protein blend, usually somewhere between pastry flour and bread flour, as most people there make bread with it. Western states mostly get the Northern blend, but, that varies. My guess is that you have Northern AP flour.
Make sure that you haven't mistakenly used white whole wheat flour, it's hard to tell apart and if it's been placed in an unmarked canister it can fool people. (happened at my house once) Not that WW biscuits are bad, they just don't have the rise of the white flour ones.
What kind of shortening? There are newer, transfat-free ones with a bunch of weird ingredients that don't really make good baked goods. (I use an all butter recipes, but, that's a different story.)
BTW, buttermilk is slightly acidic, as is, to a lesser degree, some milk. The FF recipe predates modern dairy processing. That's probably the reason for the CoT.
The other, really obvious flaw in this recipe is that it uses volumetric measurements for dry ingredients thus guaranteeing randomized results. More explanation in eG's Kitchen Scale manifesto.
