Stable value funds require slow or limited withdrawal rates. Suppose a stable value fund invests in 20 year Treasuries; as long as they're pretty sure that everyone isn't going to ask for their money back at the same time, they can plan on holding the Treasuries to maturity. They don't have to keep a liquidity reserve in case there's a run on the fund. They're also allowed to quote the maturity value of the bonds, not their current market values, and to offer the interest rates of the long term investments.
For a stable value fund to be feasible, it has to be inside of some kind of vehicle which makes it likely that those conditions will be met. 401Ks and other deferred savings plans are good places; people can't just suddenly withdraw all of their money and, as long as the stable value fund is (drumroll) stable valued, they're unlikely to panic and move it all to a money market fund.
In investing theory, there's something called the "liquidity premium," the amount you'd be willing to pay for a more liquid investment over a less liquid one. Publically traded mutual funds are very liquid investments so it's not surprsing that something less liquid costs less for a given amount of returns, i.e., the less liquid investment has better returns.
I've noticed that TIAA has begun offering a stable value fund as part of some 529 plans. They pay "only" a 1% return but your balance never changes because of market conditions. TIAA can do this because people can't generally take money out of a 529 plan all at once without paying a 10% penalty.