You can do this, actually, but it takes some serious homework. They will grant you the transit visa if you meet the following conditions: (a) your flights through the Kingdom require an overnight and/or a layover of over X hours (I forget how many) and (b) there was no faster way to get there, either on SV or another carrier. What this means is you can't just book a flight, say, from JFK-RUH-PEW, where you arrive in RUH after the one flight of the day has left for PEW, then ask for the visa. Consular officials would ask why you didn't fly carrier such and such to avoid the Kingdom altogether. You'd have to make the case that SV was the only carrier that worked for whatever reason...and there aren't many such reasons that are remotely plausible.