I bet they're referring to the objective space, not the input space.
It's easy to come up with pathological examples where that strategy doesn't help. E.g., if your objectives lie in the boundary of the unit square then the Pareto Front will have at most two points in it (near a corner -- which corner depends on whether you're looking at maxima or minima in each coordinate), but the entire set will be in the convex hull.
For a uniform sample it's more beneficial. Most points aren't in the hull (as the cardinality increases the hull density drops to 0), and in 2D the Pareto Front will be around 25% of the hull.
I'm not sure you can compute the hull any more quickly than this library in the first place, at least asymptotically, but there already exist some highly optimized solvers, so that might tip the scales a bit.
Can you elaborate on what you mean by this? Is this under the assumption of a convex Pareto front? I may be misunderstanding.