I have encountered a bizarre bug in one of my games...
A paladin of mine was somehow cloned...his clone is stuck invisibly in the upper left hand corner of the westeros map. When the hero advanced in level, his clone remained at level one. And when the hero was brutally killed ( curse you Kysar!), the clone survived.
So, right now...I have 2 heroes and a phantom paladin...which I suspect affects the likelihood of hero offers.