You deny that Matthias was chosen by the drawing of lots? Is that generally how God choses whom he choses? Or is it how man, when he has no idea what he is doing, choses?
Matthias was chosen not simply by lot. Of the many disciples, he chosen first with Joseph. Granted that then the choice between the two of them was then made by lot. While this was indeed an extraordinary method to make this choice, there is nothing in the Bible to suggest that Matthias was not truly ordained as the successor to Judas.