They're talking about the theoretical strength of SWNTs, which is upwards of 120GPa. But the highest ever measured SWNT strength, last I read, was around 60Ga - and that's the properties of individual tubes (ropes don't even approach it).
Whenever you're reading something and it mentions needing a "carbon nanotube tether", toss whatever you're reading in the "sci-fi" category. Not even the hard sci-fi category. And all for what - a ~6 year Pluto transit time? Lame.
Don't they have anything better to research?
Heck, even I can think of a more plausible approach than that - one that doesn't require unobtanium at least. Forget the "diamond anchor", land a microsat on it (approaching comet, not a retreating one). Yeah, that takes a lot of delta-V, but if it's just a microsatellite, then that's not a lot of mass. Then, forget about the "carbon nanotube tether"; use a space fountain between the large craft and the lander. Space fountains (such as paired coilguns, for example) are plausible with today's technology, requiring no unobtainium.
But the whole concept of delta-V from a comet is just not a worthwhile avenue to pursue either way. Way too much difficulty and mechanisms for failure for way too little reward.