The reverse dependency is also in place. If it gets very expensive to fly. Then the oil industry will also suffer higher expenses. And just about every single resource known is used in some way shape or form in the oil industry or supplying the oil industry. Overall high oil prices without the chances of cheap large fields to exploit leads to diminishing production because of price alone. And new discoveries are impacted the most.

Its a nasty feedback loop.

Is this really a problem for the oil industry?

If the market price for oil increases 30% the oil company’s revenue increases by 30%. Now, sure that price increase will feed into the products and services that the oil industry has to buy, but not the whole 30% as the industry doesn't only buy oil as an input.

For sake of argument, the market price increases by 30%, revenue increases 30%, costs increase 15%. Result, more profitable company.

The market bidding up the price is good news for the oil industry.

I think your treating increasing oil prices too simply. In my opinion its much closer to the way money injected in our fiat fractional reserve banking system works with one dollar of high power money resulting in a 9 dollar increase in the money supply.

So By increasing the price of oil by 30% you get say closer to a 60% hit on the price/economic side.

The problem is this revenue is declining in purchasing power because of higher prices since increasing oil prices have a inflationary effect. The direct dollar from higher prices buys less and it buys less for their supplier etc etc.
So assume in general in business supply chains are 3-5 companies deep. At each exchange you get a 30% increase.
So its 30%*30%*30% etc.

So
1 dollar -> 1.30 -> 1.68->2.17

And indeed we have seen the prices for a broad range of commodities come close to doubling over the last few years so this is probably not that far off. The reason I think it works this way is everyone is paying for the direct increase in oil prices and for the indirect increases passed on by their suppliers. So your paying for all the oil used through the whole production chain. In effect its a sort of double charge as cost are passed on. Sure profits are lowered but at the end of the day the final consumer has to pay for every drop of oil used in the manufacture of a product.
The numbers I'm using are high and it depends on the amount of oil input needed to create and move a product etc bu athe point is that higher prices for oil ripple through the whole economy causing direct and indirect price increases not just direct costs.

The oil industry is not immune and its costs increase in line with the increase in oil prices.