Evidence of modern humans existing in Israel that long ago does not mean a migration occurred. Those remains could be from a group that ranged only that far and died out.

If they can tie their genetics to the genetics of non Africans then yes, you have your evidence for earlier migration, but you still need to show that modern humans could likely have been in Iberia during the time frame of the cave paintings.

The burden of the evidence that it could have been modern humans lays at the feet of those who say it could have been modern humans, not at the feet of those claiming neanderthal did it since there is ample evidence of neanderthal populations all over Europe during this time frame.