Apple (AAPL) only opens its doors to reporters when it needs something from them — like glowing reviews for a glitzy new gadget.

What it needs right now, apparently, is a friendly account of what’s going on at the iPhone App Store, a runaway hit galloping so fast that even Apple — a company that knows a thing or two about control — is having trouble holding on to the reins.

And a sympathetic ear is what it got from Jenna Wortham, a former Wired freelancer who joined the New York Times two years ago to cover Web start-ups and mobile communications for the paper’s Bits blog.

Apple granted Wortham interviews with two senior vice presidents — Phil Schiller, who supervises the App Store approval process, and Eddie Cue, who runs iTunes — which she supplemented with material from Morgan Stanley’s Katy Huberty, Flurry’s Peter Farago, a handful of developers, and Apple’s major competitors.

Her 3,000 word piece is the lead story on the front page of the Sunday Business section, and Apple PR should be pleased. Among the highlights:

• Friendly quotes from Morgan Stanley’s Huberty (a former Apple bear recently turned bullish), who calls the App Store “revolutionary” and compares it to both AOL’s role in popularizing the Internet and Microsoft’s domination of desktop computing.
• Friendly quotes from Farago, a mobile analytics guy, who talks about Apple eliminating “friction points” in software development and distribution.
• Self-serving quotes from Apple’s Schiller, who is described — bizarrely — as “normally reserved,” and who tries to reframe the complaints of frustrated developers with the message that the review process is “a necessary evil” and that Apple is doing the best it can.
• Success and horror stories from the developers of Flick Fishing,  Tap Tap Revenge, Trillian, Bump and FreedomVoice (still waiting for approval 396 days later).
• Divergent points of view from Research in Motion (RIMM), Palm (PALM), Microsoft (MSFT), Google (GOOG) and the jailbreaking catalog Rock Your iPhone.

Wortham comes back to her Schiller notes in an accompanying sidebar in Bits that lists some of the programs on the senior VP’s own iPhone. The apps he plugs: Shazam, CNN’s app, Facebook, MLB.com, NBA Game Time, ESPN ScoreCenter, Eliminate, geoDefense and Best Camera.

Wortham’s piece may serve Apple’s interests, but for anyone who follows the mobile app scene, it’s a must-read. You can get it here.

[Follow Philip Elmer-DeWitt on Twitter @philiped]