Precisely. The medium of value delivery is irrelevant, as soon as you extract value by borrowing against an asset you have completed a transaction and therefore is a point at which it could (/should though that's the debate I guess) be taxed.
In both cases (payment in bitcoin or borrowing against stock) your remaining position could go to zero leaving you liable for tax you don't have money to pay, but that's on you to manage better.
Relevant case law: "While it is true that economic gain is not always taxable as income, it is settled that the realization of gain need not be in cash derived from the sale of an asset" https://supreme.justia.com/cases/federal/us/309/461/
It is in fact true, and clearly then doesn't mean that at all. We can and do control what constitutes a realization event, and borrowing is a pretty sensible candidate. I don't know why you're losing you mind over this fairly prosaic idea.