Petitions and form letters are not generally considered "astroturfing," because collecting genuine signatures does reflect some broad-based support. On the other hand, a well-funded PR firm with a large budget for collecting signatures is hard for a real citizens' group to match.
In early 2003, what some people consider to be deceptive form letters emanating from the Republican National Committee caused a scandal. Newspapers from Cape Cod to Hawaii were printing identical letters, all signed by local home-town people. The people signing the letters were real Republicans, but many editors and readers felt it was a sneaky way to publish Republican ads without paying for them or acknowledging where they came from. The Republicans claimed they were just helping their members express themselves.
Earlier examples of Astroturf include a 1991 campaign by PR firm Kloberg where leaked internal documents> claimed to have placed dozens of letters to the editor as well as op-eds and articles praising Mobutu's regime in Zaire (now the Democratic Republic of the Congo).