I don't know trademark law very well, but the article implied that you might have problems with that phrase. And then there's the issue of Apple's trademark giving them plausible deniability WRT filing a bogus lawsuit; they don't have to win a decision to win by outspending you.
If the phrase is altered, short and generic like "There's an app"(no-tm) rather than "There's an app for that"(tm), I don't see why it wouldn't work. I didn't see anything in the article about "There's an app"(no-tm), only "There's an app for that"(tm).