I think that it might be too strong to label the assembling of information and understanding as "magical thinking." This idea implies that there is a level of consciousness that lies outside of the human domain. I think that the power of Sophocles' characterization is that Oedipus is all too human. Oedipus' plight is not other worldly. Sadly enough, it is of this world. This is what makes Oedipus such a sad and tragic character.
Oedipus does not have to make too much in way of jumps to assemble everything together about his own predicament. The figments and fragments of truth that are given to him from others helps to allow him to understand what is happening and how he is involved. The testimony of other people, the gaps in his own perception of consciousness, as well as the lingering words of Tiresias helps Oedipus to understand everything and gain more insight into how his life connects to what has happened and what will happen. I don't think that this is magic thinking, as much as a rational being able to utilize their own understanding and capacity for thought to be able to gain insight and a sense of vision that transcends the mere physical capacity.