Well ho ho... while listening to the radio, the station I was listening to discussed this... apparently, Tom Petty's song bears an incredible resemblance to yet another song that was out a year before he released it:
The Jayhawks' "Waiting for the Sun"

AND, the Jayhawks opened for a Petty concert with that song, so Petty has heard the melody before.

Petty wants to possibly pursue legal action against the peppers? Well, he can expect that the Jayhawks might pursue legal action against him as well.

This mp3 I assembled compares clips from the Jayhawks' and Tom Petty's songs. First is Tom Petty, then the Jayhawks, then both mixed together (a very minor speed up of petty's song was required to sync them exactly...)
Clicky