Withholding this small resource does not really affect the price of oil.
A former classmate of mine makes a decent but not extravagant living tapping
coal bed methane. (And yes, before you say anything, I know these guys are reviled in many places for messing up the water and tearing up the landscape.)
But coal bed methane is not a huge resource, it accounts for maybe 7% of U.S. natural gas production. The price consumers pay for natural gas is not greatly influenced by coal bed methane production.
Anecdotal stories of oil wells being drilled and capped off are often passed around as a way of reassuring people that everything is all right, that there's still plenty of oil in the ground. But that's not true. A small oil or coal bed methane field in the Rocky Mountain is nothing like the huge oil and gas fields we have tapped in Saudi Arabia, the North Sea, and so on.
All of the huge oil fields in the continental United States have probably been found and mostly drained. U.S. production peaked in the 'seventies, and now we face diminishing returns no matter how many holes we drill, no matter how many people like my former classmate swarm out into the field.
If someone out there is drilling holes and capping them off in the hopes of making money as the price of oil goes up, it is probably of no consequence to the overall price of oil. We cannot significantly reduce the price of oil by increasing U.S. production. We passed that point long ago when we foolishly elected Ronald Reagan as our president.