So block 125125 was a chance occurrence yes, but if mined today that 18 billion diff mean it would be accepted?
Right. It doesn't have an 18 billion diff, but the hash value is low enough to be accepted by such a one.
It also isn't the lowest block hash yet.
2013-10-27 14:55:42 SetBestChain: new best=000000000000000000028c32e6952731326747bae4be8db0f832d6eea0362050 height=266381 log2_work=73.237967 tx=26093998 date=2013-10-27 14:49:44 progress=0.999972
Is vastly lower, and would be accepted by a difficulty of ~110,484,089,548,580.
Wow...it was news back then with block 125125, but never saw anything about this one. Still, I do believe I answered correctly given the question and the fact that I didn't know about this new block.
EDIT:Oh, apparently block 125125 would've been valid for ~35 billion difficulty. Well, my memory wasn't right apparently.