That's not what they're using here. A chain saw uses a chain with cutting blades attached. As the chain moves, it drags cutting blades against whatever you're cutting. The hedge trimmer you describe uses a reciprocating motion to create something more like a bunch of scissors, and the size of that opening limits what it can cut.
This helicopter is dangling a powered cutting bar with 10 saw blades on it. Think of the blade on a table saw, skill saw, or something along those lines. Those blades would happily cut into anything softer than themselves. If they were to hit the powerline, it'd make a big mess of sparks. Maybe the blade would glance off, or maybe it would grab enough of the cable fibers to begin unraveling it. Either way, the goal seems to be to keep away from the wires.