It's nonsense to claim that "stat arb" means "pairs trading."
Pick a market. You estimate vol to be 20% sampled close-close. You estimate vol to be 10% sampled hourly. Based on your stats (estimates), there is an arbitrage. It's only as risk free as your stats are flawless and a given (that is, not at all). But there may be edge.
So you sell the ATM straddle and delta hedge close-close, while also buying the ATM straddle and hedging hourly. Net net, no options at all, just a net delta hedging strategy in ONE underlying.
Stat arb gets its name from imposing a distribution on a market and basically pretending that's the real world. It's first moment arb -- a coin flip with expected P&L >= 0. But all good trades start with a positive expected P&L. You still have to have a good model to derive said distribution and be able to contain variance. It's not risk free, but if you stay alive and don't blow up then the central limit theorem says you should make money over time.