This has little bearing on the point of zen baby's writeup, but I feel it has to be said: the vast majority of pagans utterly disdain blood magic, or consider it something very sacred and not to be undertaken nearly as lightly as most Christians might take swearing on the bible... even if they do mean to tell the truth. Even the disturbingly amoral Temple of Set disapproves, largely because anyone who draws energy from harming others is likely to be unstable and thus not optimally effective.

I would also suggest that anyone who swears on a holy book or icon, and does it sincerely, is really swearing by their honor. They are not necessarily attributing power to the object, but perhaps to the reverence and inner strength that their devotion inspires. They are linking their oath to a sign of their belief, as if to say that defiling their word would also defile their highest and most dear principles.
As ratbastid points out, usually simply speaking words is not considered utterly binding. For some people it is, because their highest principle is the sanctity of their words. For others, swearing on something holy or of great value is a way of affirming the importance of this utterance in particular.