I was working in Saudi for a bit in 2002. Very strong view from the locals there was that they hated Saddam and a lot of what he did, but accepted he had the region by the balls, preventing the extremists rising and that taking him and his regime out would instantly destabilise the whole region.
I was working there for a bit, as well. 2 years between 1994-96. 2 and a half hours a day work and 26 weeks a year holiday. Tax free. Not a bad job. No wonder I got my 5k and 10k pbs at that time.
But back to the point. Saddam fired a couple of scud missiles into Riyadh during the first Gulf War but the Saudis weren't too keen to fire back as you said. The Saudis also heavily bombed a few of their own towns North of Riyadh in 1994 to stop fundamentalists.