The proposed resolution to the paradox is that actions that would create paradoxes are excluded by quantum mechanics -- they have zero probability. Assuming that the proposal is valid, my comment was:
One advantage of this idea is that it is analogous to an established quantum mechanics principle, the Pauli exclusion principle.
The exclusion principle is the observation that, if you calculate the probability that two electrons will occupy the exact same quantum state, QM gives a zero probability. It doesn't matter what the state is, you always get zero.
This is why solid objects can't pass through each other, why, for example, you don't fall through the floor and keep going to the center of the earth. Solid objects are solid because almost all the available electron states are filled. If you try to push solid object A (the sole of your shoe) into the space occupied by solid object B (the floor), there are nowhere near enough empty states to accommodate all the electrons in object A. Therefore, you're trying to push many of the electrons in A into states already filled by electrons in B, and the probability of that happening is zero. So you stay above the floor.
Analogously, Lloyd et. al. propose that the probability of you preventing your own birth calculates to zero. You're trying to introduce an additional cause (a bullet in your grandfather's heart) into a sequence of events that already has 100% of the causes it needs. And like the way the floor is shoeproof, you'll find your grandfather is bulletproof.
Actually, I expect that the past is travelproof. Any travel into the past, however innocuous your intentions, will introduce paradoxes at the quantum level. And QM cares about those at least as much as it cares about you and your grandfather.