.005" to .007" allows room for the rotating assembly to grow as it heats up, and it also allows the proper clearance for lube to get in there and do its job. There is always (hopefully) a microscopic cushion of oil between the teeth when it is spinning...getting compressed and flung around. Too tight of a tolerance will generate excessive heat, and the assembly can grow and cut your backlash clearance down to something less than adequate. You'll know immediately (within 1000 miles) if something wasn't right. Look for "bluing" on the teeth and obviously shavings & dust particles, from the teeth being pushed too deeply into each other. Also look for sharp edges on the teeth...a good indication they were too tight. Most of the time people think tighter clearances on machines is better. Most of the time that's true. But on backlash....
Too much clearance is bad.
Too little clearance is very bad.
The problem with running on the slim-side of backlash is this: ZERO is always ZERO. At only .003"...you're real close to .000". It doesn't take much expansion to close-up that small of a space. For this reason I like em on the loose end of the range (.008" to .012"). This keeps things nice & slippery...cool running...minimal drive loss...even after being heated up, there's lots of space for lubrication. Either way...there is a suitable range .003"-.010" and a preferred range of .005" to .007"...and you know em both, so no excuses! Your guy should know them too, and if he says its good...you should take his word. On the other hand you can easily verify it yourself with minimal shop tools. Its super easy and does not require any dis-assembly. All you need is a dial-indicator and a magnetic base...
[video=youtube;CZS6Rc0Omgo]https://www.youtube.com/watch?v=CZS6Rc0Omgo[/video]
Do this check on 5 or 6 teeth all the way around the ring gear. They should all be within .002" of each other, and you should arrive at an average somewhere between .003" and .010". If any of your readings drop below .003"...then you have a tight spot, and its worth taking a closer look.
Lastly...I have never heard of the "as it wears it will loosen up a bit to preferred spec" method. Its a ring & pinion...not a fat girl trying on designer jeans!-LOL Its either in range...or not. Period. That's why they give that info to you. Toss that AAM-7 in your truck...run it over to the nearest machine shop and throw a dial on it. Its a five-minute check. Worth it for the piece of mind.