This is a myth.I don't know who started it, but it is an example of weak grasp on economics fundamentals.
Any increase in price of any widely used commodity increases cost of living.By a corollary to that, any increase in tax increase cost of living. Oil is not much different in this respect.
But an important point people miss is that it is total taxation burden which is correlated with cost of living, not a single tax or increase.Also, Government has to collect revenue for functioning, and taxes are biggest source of government revenue. Government could collect that revenue by imposing tax on oil, or could collect same revenue by imposing extra tax on finished product. Increase in Oil price would lead to general increase in price by way of adding extra transport cost, but if government keeps oil prices low and yet impose higher taxes on finished goods, it would be more detrimental for economy than imposing higher tax on oil products. The reason for this is that it would lead to addiction to Oil due to usage of inefficient old machinery and increased consumption, and tax evasion as evading tax on finished goods and services is easy than evading taxes on petroleum.
