No, but they ARE interfering in what is as yet an issue for the 9th circuit. Given that they almost ALWAYS strike down 9th-circuit rulings, stepping into the case says to the judges of the 9th: "We're watching you. Do the right thing."
The stay is pretty much SOP. It has nothing to do with the 9th Circuit; it would've been issued regardless. And the Court doesn't "almost ALWAYS strike down 9th-circuit rulings". The 9th Circuit decides thousands of cases each year. The Court overturns maybe 1.5% of those.