P-C, I'm keeping my fingers crossed, but, yeah, there's a slight possibility that you may be SOL. My advice as a Bay Area renter of some standing is to (a) get a copy of your credit report ASAP, run off extra copies, and carry one with you to every single apartment you see; then, (b) if you're interested, get an application right that minute, fill it out, and hand it right back to whoever's showing the apt. along with the copy of your credit report.
The apartment-hunt dance is not as bad as it used to be in the mid-90s, when people would just show up at apartment showings with first, last and deposit in cash in their back pockets just in case they liked the place, but it's still kinda competitive for the really nice places.
But you still may get this one anyway. Just, if you don't, go at the next one fully armed.