There's actually some science to those issues, but they played with it. The heavy radiation from the Pulsar *would* be blocked by sufficient amounts of the ship. The only spot that was fully protected was the garden? That's not going to work. I kind of mentally hand-waved it as 'the only sufficiently protected area that currently has life-support'.
My knowledge of astronomy is amateur at best (as can be seen from other posts here

) and I know pulsars aren't fully understood but there were a few issues I had:
1) If they were close enough to the pulsar (likely emitting high-energy x-rays, but not necessarily) so that vaporization would happen, I would think that the whole ship, underside and all, would be in the field of the "burst". I know pulsars are smaller than the Sun, but they're still on the scale of kilometers. They had to be relatively close for the energy to still be high.
2) It's my understanding that pulsars spin
fast, and that's what gives them the energy to emit radiation. Fast in this case would be on the order of seconds, not minutes or hours.
3) Assume that Destiny is full on facing the pulsar so that Scott and Greer
could run to the underside of the ship and be safe from the sweeping motion and width of the radiation beam. The shields were already shown to be failing (in parts one/two) which means there were
still areas radiation was leaking through. Presumably this radiation goes through the ship (hence Rush's plan works) and so even by being on the underside, the likelihood is fair Scott and Greer
still get caught in the burst.
Meaning, ultimately, that the pulsar (and Scott/Greer's escape) was a giant
deus ex machina on the part of the writers. I suppose looking back I wasn't unhappy with the science hand-wave part so much as the blatant nonsensical nature of it. Like I said, I'm just accepting it and moving on.