At these time scales, background radiation is the fundamental killer, and it is omnipresent in the environment.

Using numbers taken from http://news.mit.edu/1994/safe-0105 for napkin-math:

Average background dose/year: 500 millirem

LD50 instantaneous exposure: 450000 millirem

LD100 instantaneous exposure: 600000 millirem

Radiation exposure of our dinoDNA sample: 65 million * 500 = 32.5 billion millirem.

Obviously there's a lot more to it than simple dose adding, but this gives you an idea of just what deep-time DNA recovery is up against.

At least on the ancient DNA projects I've worked on, the main obstacles have been a) deamination, b) fragmentation, and c) environmental contamination. Maybe radiation enters the picture at Jurassic timescales, but the DNA would become completely degraded and worthless tens millions of years before that. Unless they somehow managed to find a dinosaur frozen at about 0K, I'm extremely skeptical of these claims.

Right, but even a small amount of water (and presumably, ice) is amazing at absorbing radiation. Wouldn't something buried in a few meters of ice or more be effectively insulated from radiation?

DNA isn't isotope free.

Like hyperbovine mentioned, there are actually other effects that come in to play far sooner, but radiation puts (an additional) hard cap on things, and is easy to napkin-math.