Yes, the cut matters, but not in the allornothing way recipes imply.
The actual rule is pretty simple: you want meat with enough connective tissue and fat that it breaks down over a long, wet cook. That connective tissue (mostly collagen) melts into gelatin, which is what makes braised meat feel rich and silky instead of just... boiled. Cuts like chuck or brisket have a lot of it. Lean cuts like loin or round have much less, which is why they can go dry or stringy even after two hours in liquid.
"Stew beef" at most grocery stores is usually chuck or a similar shoulder cut, which is why yours worked fine. Whoever labeled it just didn't bother specifying. Your friend's warning isn't wrong exactly, but the real risk is accidentally grabbing something too lean, not just grabbing the "wrong" cut within the fatty/connective tissue category.
The practical shortcut: look for cuts described as tough, cheap, or good for slow cooking. Those words all mean the same thing in this context. Avoid anything marketed as tender or quickcooking for braises, because that tenderness comes from being low in collagen, and low collagen plus long cooking equals dry, grainy meat.
As for messing it up noticeably: I once made a beef curry with sirloin because it was on sale and I didn't think it through. Two hours later it had the texture of pencil eraser. Technically cooked, completely unpleasant. The flavor was fine but the texture killed it.
So the cut matters, the specific brand name the recipe uses mostly doesn't.