That's what I'm thinking too. Of course Jon wouldn't go publicly and say that he just rehashed an old song when he was asked by producers to write one for the movie. But that first line in Always has struck me by feeling out of place since the beginning. After these quotes, I think that Always really might've been some sort of left-over/unfinished idea from the KTF sessions that may simply not have been fitting / not deemed good enough for the record.
So Jon pulled it out, altered the first line to fit the movie and then said it was written for it.