Question: A typical modern scenario of the medieval siege was the throwing of oil on the attackers from ramparts. Oil was really expensive so why waste it on attackers? Most commonly the items thrown were boiled sewage, rocks, and arrows. Does anyone know of any primal source of evidence of boiling oil being used as a weapon in sieges?

Answer: 
Boiling oil is a good weapon, because its boiling point (400 degrees Fahrenheit) is much higher than that of water (212 degrees). 

It was a moderately effective weapon against men. But by its boiling and burning properties, it was a very effective weapon against ladders, rams, catapults, and other war instruments made of wood. Also, if successfully used, it would cause a horrible death by burning. As such, killing ten enemy soldiers with oil had more of a "deterrent" effect than killing the same number by sword. 

Because it was expensive, a garrison would not base its plans on using oil. But they used oil for other things like cooking, which is to say, that it could also be used to "cook" their enemies. When one is under attack, one uses what weapons one has at hand and worries about the consequences later.

An attack on the citadel was basically the last day of the battle. Either the defenders would win, in which case they could exit the place and replenish their supplies of oil, or they would lose, in which case they'd be slaughtered. Either way, saving oil for "after the battle" didn't make sense.
Incendiary devices were frequently used as projectiles during warfare, particularly during sieges and naval battles; substances were boiled or heated to inflict damage by scalding or burning. Other substances relied on their chemical properties to inflict burns or damage. These weapons or devices could be used by individuals, manipulated by war machines, or utilized as army strategy.
The simplest and most common thermal projectiles were boiling water and hot sand, which could be poured over attacking personnel. Other anti-personnel weapons included hot pitch, oil, resin, animal fat and other similar compounds. 

* Smoke was used to confuse or drive off attackers.
* Substances such as quicklime and sulfur could be toxic and blinding. Sulfur- and oil-soaked materials were sometimes ignited and thrown at the enemy, or attached to spears, arrows and bolts and fired by hand or machine.
* Fire and incendiary weapons were used against enemy structures and territory, as well as personnel, sometimes on a massive scale.
* Large tracts of land, towns and villages were frequently destroyed as part of a scorched earth strategy.
* Incendiary mixtures, such as the oil-based Greek fire, could be launched by throwing machines or administered through a siphon.

Some siege techniques—such as mining and boring—relied on combustibles and fire to complete the collapse of walls and structures..