My model of the oil market does not predict a relationship between speculation and inventories. Paul Krugman must have a different model in mind. My guess is that it is a reasonable model, and that he will explain it at some point, perhaps on his blog.
Meanwhile, here is my model.
Think of there being two prices for oil; the forward price, say, for delivery one year from now; and the spot price, for delivery today.
The forward price reflects the market's view of long-term fundamentals in oil production and oil demand. Relative to that, and to other factors such as the interest rate, there is a normal inventory of oil along with a normal spread of the forward price over the spot price. The spot price is bid up to the point where refineries are just willing to hold the normal inventory. If the spot price is unusually low relative the forward price, then they hold above-normal inventories until spot prices rise. If the spot price is unusually high relative to the forward price, then refineries try to unload their inventories while they can get a good price.
In that model, I don't see how the level of inventories relates to the level of prices at all. I only see how it relates to the discrepancy between the spot price and its normal relationship to the forward price.
I assume Krugman has a different model. As to his larger question of whether the price of oil represents a bubble, my behavior shows that I agree with him that it is not. I would not dream of buying put options on oil futures, which says that I do not think that oil is clearly overpriced. However, I do not look at inventory levels as an indicator of whether or not forward prices are a good predictor of spot prices.
Suppose that the forward price of oil were ridiculously high relative to long-term fundamentals. In that case, I would expect refiners to bid the spot price up to ridiculously high levels also, while holding a normal level of inventories.
UPDATE: The first comment leads me to dredge up this old post on how oil companies should be using futures prices.