Rystad like many others use Cash Flow as reported in quarterly and annual reports simply because that is a number that is apples to apples. That doesn’t mean a comparison of that number tells you what is going on. As I said cash flow includes all cash costs plus accounting non-cash items.
E&Y show the reinvestment of cash into operations in a different manner. Their ploughback equation looks at revenues net of costs and then how much of that is expended back into the operations through OPEX and new E&P CAPEX. Basically they are putting back all of their revenues into the business as would be expected of publicly traded companies who the share holder expects to grow.

Just as a good example of what is going on the E&Y study summarizes the top 50 US oil and gas company results. Looking at the first entry Andarako.
Their results of operations were $1,962 MM for 2018. That would appear on their balance sheet as free cashflow. But when you start to look at the entries you see revenues were $9,071 MM, production costs were 2,415 MM, exploration expense was 417 MM, DD&A was 3,198 MM, impairments were 373 MM, other income expense was 121 MM and income taxes were 585 MM. If you remove the non-cash accounting items (in this case DD&A and impairment) you get a better picture of what the company is doing (I’ve previously pointed out that when you are doing your own home budget you do not include the depreciation of your house or car in that calculation as it is meaningless to the bottom line of what you can afford to do). Hence on a cash basis before tax Andarako saw $9,071MM - $2,425MM - $417MM - $121 MM or $6,045MM a number much larger than what would appear as cashflow in the balance sheet, the difference being non cash accounting items. It is pretty obvious that they can afford their own E&P programs.