Satoshi did not technically solve the byzantine problem, merely solved it in a probabilistic or pragmatic manner with game theory where someone is incentivized to secure the network instead of attack it.
Yes that's exactly right and I explained this on another of one of r0ach's thread spam Sybils.
There is a globally unique longest chain, although your confidence that you know what it is depends on the distribution of hash rate in the network.
The issue of resistance to attack is one of a tradeoff between concentration of hash rate and the rate with which confidence in an apparently-longest chain being the correct chain increasing over time. This is seen in Satoshi's paper where he analyzes the case of a single 45% attacker and concludes that you would need to wait 340 confirmations for 1/1000 confidence (which isn't even that strong if the exposure is high).
He doesn't generally discuss the question of concentration though, outside of an explicit "attack". In fact the issue has broader implications.
There is an enormous amount of concentration now
that does't come from pools. This has the same effect of weakening the security model that pools do, or possibly worse (since you can't pull hash rate from KnC if they decide to misbehave).
In the future this will likely evolve in one of three ways: 1) increased concentration, decreased value and increased irrelevance; 2) continued equilibrium between some degree of "acceptable concentration" and limited value and relevance; or 3) a break from the status quo where concentration decreases due to limits to economy of scale and commoditization of ASICs along with increased value and relevance (perhaps enormously so).