She's been in Celebrity Rehab less than a week, and Rachel Uchitel has already licked her addiction to prescription drugs ... yup, Dr. Drew is just that good!

Actually, she was never was addicted in the first place.

That's the rumor stemming from Celebrity Rehab with Dr. Drew, where sources close to the production say she never really had a pill-popping problem.

It was reported earlier in the week that she was hooked on Ambien - a sleep aid she'd used during feverish sex romps with Tiger Woo...