I do not think anyone claimed that scientific discoveries or theories (like Einstein's) could be gained by "pure intuition".
Rather, there is a body of knowledge like maths, logics and a few other very general principles (also of morals) that logically precede empirical knowledge. Until the 18th century most thinkers in most cultures believed that some "natural theology" also belonged to that kind of knowledge. It's not necessarily "innate" but it can be established by reflection on very general features of the world we experience or on very general principles we need in any case to establish any knowledge at all. Therefore the core of such "metaphysical" knowledge is not to be understood as idle speculation, neither can it be in contradiction to empirical science.
But it cannot be "disproved" by empirical science as empirical science cannot disprove mathematics. It could merely show that a certain type of mathematical scheme would not be applicable to a certain domain of empirical nature but to argue for something like that the scientist would certainly have to use forms of logic (and probably also mathematics), therefore again has to presuppose the validity of some bits of non-empirical knowledge.
But it can probably be safely said that it is very hard to derive specific ideas about afterlife, punishments, karmic retributions etc. from general metaphysics or "natural theology" (unlike arguments for a "prime mover", "Absolute Being" or sth. like that). This was largely the domain of "revealed knowledge" and religious thinkers would try to show that it is compatible with the more general metaphysical framework that could be established from reason alone.
(For me as a layman it is also fascinating how unspecific and inconsistent e.g. the christian scriptures are with respect to "afterlife" etc. Most of the new testament is much more concerned with eschatology, i.e. the End of the World (as we know it) and the Kingdom of God was expected to come very soon and not the end of individual lives, immortal souls etc. It took a thousand years of theology to arrive at Dante's sophisticated model of hell, purgatory and heaven.)