That's not at all what Blizzard itself states. For example, when you go through the introduction for Halls of Reflection, the ghost of Uther states that Arthas is merely a weak and diminishing voice amongst all the other souls captured by Frostmourne. He's not dominant (or even close to) in any way. He's not even in a position to contend for domination, he's been vanquished. Period.
I believe the official story goes that the first Lich King WAS Ner'zhul, or rather his soul - twisted and tortured into madness by Kil'jaeden - and then imprisoned into that suit of armor which Arthas later put on when the merging occurred.
Arthas' soul was consumed by Frostmourne when he became a deathknight, so when the two merged, Arthas' body would become the host for Ner'zhul's spirit methinks. Both were changed in the joining, but that old orc shaman should still be in there somewhere...
Bolvar's soul was never consumed by Frostmourne, so perhaps he would be able to resist Ner'zhul/the Lich King's influence or even control him. After all, Bolvar was a true hero and man of good, unlike the flawed and morally unsound Prince Arthas. Bolvar's spirit should be much stronger than Arthas' was (who let himself be manipulated into committing atrocities even before taking up Frostmourne...)