Different Free Cashflow Calculation via net income - THE real free cashflow?

I recently read in a finance book about a "different" free cashflow calculation which I didn't really get. However, this is not about the free cash flow calculation used in a DCF via NOPAT, but rather about the “actual free cash flow, as it really is.”

First, the interest result is subtracted from net income, taxes and depreciation are added back, and then we arrive at EBITDA. From there, changes in working capital, capex, other cash positions that are not deducted in the P&L, as well as other non-cash items from the P&L are added. According to the author, this already gives us the free cash flow to the firm.

But taxes haven’t been subtracted – they are still “included” – and I don’t really understand how this can be considered the “actual” free cash flow, because obviously a company has to pay its accrued taxes, so that portion isn’t actually available.

I’ve never seen this free cash flow calculation used anywhere else, and I’m wondering whether the author is just trolling a bit here or if there’s some real logic behind it.