He needs to lawyer up it seems. Get a lawyer to send Apple and the competitor a note on letterhead saying that the dispute is without merit and that if Apple proceeds with pulling the app, there will be hell to pay.
Lawyers are expensive. Then point of the article is that Apple could, quite cheaply, have done their homework and he wouldn't have that large expense. iPhone development - it's not cheap, once you factor in the lawyer.
Are you an iPhone developer? Do you want a similar, competing application out of the App Store? Do you want to spend the next 18 months of your life in court, instead of developing applications? All you need to do is send an fraudulent infringement claim to Apple.
This doesn't appear fraudulent in any legal sense.
DMCA: recipient pretty much must act under the assumption it's legitimate, legal action can be taken against someone who files one fraudulently.
This case: Apple is free to apply common sense, but no guarantee they will, and no legal action is really possible against "someone sends something making vague claims of proprietary technology".
It doesn't use any magic phrases that have meaning, like "patent pending", and it doesn't claim to be a DMCA takedown, so if Apple decides to yank an app, that's between Apple and the developer they screwed over.
Whether or not your infringement claim was really based on reasonable evidence is something we'll find out in discovery, won't we? If you get Apple to remove my software from the app store, and I sue you (and I almost certainly will), and it turns out that your claim to Apple was frivolous, your liability is going to be sick.