Why is Aggregate Accruals = Change in Net Operating Assets

For the life of me, I do not understand how, using the Balance Sheet approach to computing accruals, we have: Aggregate accruals = ∆NOA, where

NOA (net operating assets)
= Op. assets - Op. liabilities
= [Total assets - cash(*)] - [Total liabilities - Total short and long-term debt]

(*) “Cash” includes cash, equivalents, and marketable securities.

I get that if you make earnings that are not cash-based (like credit sales), these will increase NOA by increasing OA. I also get that if you make earnings that are cash-based, these will not affect NOA because cash is not part of operating assets.

BUT, what I don’t get is that there are apparently ways of affecting NOA with zero accruals-based (non-cash) earnings.

For example, if I borrow 1 trillion dollars and then immediately use the proceeds to purchase PP&E, then NOAs will increase. Indeed, operating assets increase (because total assets increase by 1 trillion, whereas cash doesn’t change), but operating liabilities don’t move (since both Total liabilities and total debt increase by 1 trillion, which cancels out). So there you have it, I have 1 trillion in aggregate accruals (= change in NOA) without having made any accruals-based earnings at all. What on earth am I missing?

Why is Aggregate Accruals = Change in Net Operating assets?

Related (basically the same question), but the answers are not really helpful unfortunately: