I agree with this statement...to a point.
Certainly I've taken some outstanding pics with my Nikon D3000. Heck, aside from the lack of RAW image support, I've taken some real keepers with the camera on my iPhone. Certainly, any reasonably skilled photographer can produce decent images using any camera. HOWEVER...
It's important to recognize the limits of the equipment you're using. While the D3000 and iPhone 5s can take good (and even great) photos under the right conditions, I've yet to produce a satisfactory image from a dark ride. Trial and error and fast glass have given me some ho-hum dark ride images, but nothing spectacular. (And no, I *NEVER* use the flash.)
I now recognize the limits of the D3000 and am in the market for a slightly better camera. Like the OP, I have a restrictive budget...so I'm not buying top-of-the-line. But based on reviews, the D7000 might get me closer to my photography goals. And I can get a body-only for well within my budget. (The D7100 pushes my budget a bit too much or else I'd jump to that.)
Anyhow, I just wanted to give my opinion that any equipment can produce awesome photos, but it's important to (1) understand how to properly use it to get the best results and (2) understand its limits. Also, any advice on the D7000 (or other Nikon equipment in that same price range) would be appreciated.