A risk-free hedge is a deal made with a counter-party. These deals are promises all the way down and create counter-party risk which means they are not really risk free. See this article on the Money View of credit and debt relations which is different from the assumptions underlying modern finance theory:
https://lpeproject.org/blog/promises-all-the-way-down-a-primer-on-the-money-view/
Further, unlike the Money View, the Portfolio Choice Theory (such as that developed by James Tobin), which is at the heart of asset pricing models, entirely abstracts from the role of dealers in supplying market liquidity. These models assume an invisible hand that provides market liquidity for free in the capital market. From the lens of supply and demand, this is a logical conclusion. Since a supplier can always find a buyer who is willing to buy that security at a market price, there is no job for an intermediary dealer to arrange this transaction. The Money View, on the other hand, identifies the dealers’ function as the suppliers of market liquidity—the clearinghouse through which debts and credits flow—which makes them the primary determinant of asset prices.
Technically it is not possible for a risk producing venture to borrow at the risk free rate. However, as Warren Buffet explains (lost the exact reference) a well managed insurance company may have cost of capital below the risk-free rate. This is because the premiums charged for an insurance policy are capital for use in operations of the firm and the payouts for insurance claims are contingent future outlays. So if the insurance company can manage investment risk, costs, and actuarial risk it may have a cost of capital below the risk free rate.
I would add that the federal government in the United States tends to insure the ventures which would not be sound on an actuarial basis to provide long run profits to a profit-motivated insurance firm. These government subsidies include federal loan guarantees, flood insurance, and deposit insurance. During the so-called global financial crisis starting in late 2008 the Federal Reserve had to take over AIG derivatives book and the US Treasury became conservator of Fannie Mae and Freddie Mac. Perry Mehrling calls the central bank the financial dealer of last resort and I refer to the US Treasury as the investor of last resort. If the counter-party has a cash flow crisis or must be resolved due to insolvency then the risk-free hedge deal suddenly has "fat tail" default risk.
This article provides a "narrative" for the demise of AIG as financial dealer with lack of liquidity in a financial crisis:
https://insight.kellogg.northwestern.edu/article/what-went-wrong-at-aig
The global financial crisis and its resolution is a case study which tends to validate the Money View wherein financial dealers use their balance sheets to create liquidity and these dealers run out of liquidity when there is a general panic of investors who hold the liabilities of the dealers (rollover risk). The risk-free hedge will have "fat tail" risk whenever the counterparty runs out of balance sheet in the network of financial deals.