No, you can audition as a civilian and *then* go to basic/AIT. At least that's how most do it(myself included). Hell, in the Airforce the band folks have a separate basic training from everyone else?! I joined the wrong branch of service! Bahahah
Yeah, the OP is wrong on this. You still have to be able to read despite what they might have told him, just not for an incoming audition. I just got out of the active duty band after 8 years(now in the reserves for another 6), my audition liaison told me "yeah, don't worry about sight reading as a bassist!" and heard the same thing all through AIT at little creek. During concert band they'd tell all the rhythm players to go "IP" (individual practice) in the pods on the 1st deck(it's at a navy base)... really though that was setting up many for failure down the road.
A little background on myself: I went to a music school before this and struggled with reading(still do) but got a scholarship despite my shortcomings! In AIT(advanced individual training) I recieved the C1(Charlie 1) identifier which means you are considered "excellent" by their standards also despite the gap in my knowledge/skills!
Got to my 1st band at Ft Bliss and first rehearsal was with the big band, no chord charts and all written out lines! I had my ass handed to me, it was embarrassing to say the least! The 1SG was like "I though you had a C1? What gives SPC Hintz?" LOL. Eventually I got better at reading and now I'm much more comfy with it to a certain extent!
For an incoming audition they don't test sight reading like they used to so I think the OP will be fine! When I did it they let us pick our prepared pieces so I picked "Havona", "YYZ" and "Smooth". Just practice your ass off, forego some sleep and 5 songs ain't nothing in a week! You can always get caught up on sight reading down the road, the main thing they want is that you sound good and can learn songs quickly!! Good luck!!