Not only is the thumb-width rod a load of grotesque bunkum, it's also pretty obvious bunkum. It is, admittedly, provoked by an accident of the English language; or strictly two. Firstly, English is one of only very few Indo-European languages where the words for »thumb« and »inch« are not either one word, or obviously related; the reason is that the ancient measure of the inch, far predating standardized weights and measures, is derived from the length of the upper joint of the thumb. Of course this varies a bit, but before centralized authority, common things like your own body are all you have to work with; see also foot, ell.
The second reason is that »ruler« has increased in its meanings fairly recently. It used to be that a ruler was only the guy who was the boss of all of you; and the wooden instrument with equidistant markings was a rule — in fact, the other usage of the word rule, as »guideline« or »regulation«, is a figurative one springing from the instrument sense; terms such as »slide rule« still bear witness to this circumstance. (In fact, »regulation« is in itself just a way of saying »measurement with a ruler«, since the word rule is related to the Latin »regula«, meaning, you guessed it, ruler. So a regulation is the use or product of a ruler. The figurativity runs so deep it's impossible to even explain myself without tautology.) Unfortunately, the use of »ruler« has now obliterated that of »rule« to such an extent that people no longer intuitively recognize a »rule« as a flat, straight rod with distance markings; and that completes the confusion.
So, in summary, the »rule of thumb« is the top joint of your thumb, the ruler with which you measure out the inches when there's nothing better available. It's imprecise and it's unscientific, but it often gets the job done.