I like "sweepsfoot"! Very descriptive.
Yes, a straight edge is one of the defining characteristics of a sheepsfoot. It really annoys me when manufacturers call a blade with a belly a "sheepsfoot". A straight edge is easier to sharpen and cuts better in many applications than a curved edge.
But it is hard to find a really straight edge. I have been looking at several "sheepsfoot" blades that happen to be near at hand, and the only one that has a really straight edge is a Spyderco Salt 2. Even the Caribbean has too much curve, contrary to what I said earlier. The EDZ is close to having a straight edge. The Civivi Chevalier and Vosteed Valkyie are fairly close. The Hogue Decca and the new Kershaw--I can't remember what it's called--are borderline.
A knife that has a forward-facing, stabby point is NOT a sheepsfoot. I particularly like a sheepsfoot when I am working around livestock because I do not want to accidentally stab anybody. The sweepsfoot blades miss the whole point of a sheepsfoot point being angled downward, not forward.
Traditionalists may also complain that most of the non-traditional knives that are called a sheepsfoot are closer to a lambsfoot. But even Spyderco does not have a sheepsfoot with mostly parallel edge and spine that I know of.