In 2006 there are a few recordings where he sang "ain't" and he definitely does in the videos above. It's not a thing limited to 1995. I'm sure there were other later appearances of it as well.

The official lyrics have been, as Captain_jovi pointed out, wrong on numerous occasions. My bet would be that songs got altered even after the lyrics had gotten submitted. Take Bitter Wine as an example. People had wondered for years why the lyrics in the booklet differed from the final cut. When the electric demo of the song was posted we realized that those alternate lyrics still stemmed from there.
Or the most recent examples on This House Is Not For Sale.
There was an edit of the title track on radio stations where Jon sings
"baptized in a muddy river, not a wish in the well..."
yet the album version is
"The door is off the hinges, there's no wish in the well..."

Or during God Bless This Mess: the lyrics say "and good men stood at your side", while he's actually singing "still they're at your side".