For context, some of the numbers here:
c: 300,000 km/sec,
1/3c: 100,000 km/sec
Fastest man-made thing in history by far, Voyager 1: 17km/sec
Time it took most recent Mars mission to get there (Mars Science Laboratory, 2011): 254 days
Closest Mars-Earth: 182 light-sec
Farthest Mars-Earth: 1342 light-sec
These scientists are proposing to send something at about six thousand times faster than anything man-made has ever gone in history. At this scale, the energies involved become absolutely insane. Guess what would be the energy of a tiny one-gram pebble floating in space hitting this spacecraft? Ten terajoules. That's approximately equal to you walking along on your way to work and getting hit by, oh, I don't know, the International Space Station (13 terajoules) or a sixth of a good sized atomic blast (63 terajoules). Space is a busy place. If you hit even one thing, you're over.
But, you argue, you won't get hit by any pebbles. I'd imagine that you're wrong, but let's humor you. You argue that the largest thing to hit you would be a microscopic 0.001g object. Let's say that your microscopic object is standing perfectly still in space, somehow, even though that's incredibly unlikely.
You hit this object, and instantly your craft is subjected to a ten gigajoule blast. Let's put that into context: at an incredibly small point somewhere on your craft, rocketing along at just north of 223000000 mph, you just experienced a hit equivalent to one hundred million large caliber (.45) bullets. Let's say the scientific payload of your craft is one gram, and the rest is armor. You'd be safe right? No, unfortunately 99.999kg of armor doesn't seem so strong in the face of one hundred million bullets.
I don't think it's possible.