The argument is that he wins against Palin due to Democrats, who wouldn't have voted in the primary, preferring Begich over Palin.
Now I'm not sure if Alaska was semi-closed, but that's not moving the needle as hard as you want it to. Because if you're already registered for a party, you cannot vote in the other party's primary. Only unregistered voters may, and only in one.
And typically, independent voters don't do that. As reflected in the low vote totals in the various primaries in previous elections.
The two-tier primary/general election system produces more extreme-position winners, exactly by this mechanism.
And consider another common outcome - shift the odds very slightly here and the Palin-esque candidate wins the primary, and the general, even though the eliminated primary candidate (Begich in this case) would have been more acceptable to the electorate at large.