I found an interview with Carter published in 1999; it's not clear to me when the interview was actually taken, but it certainly was after 1990 because he mentinoed the Gulf War. Anyway, in this interview Carter said:
And the fact that we developed... and I even announced, during my last year in office, that we had developed the technology for the Stealth aircraft, which makes them totally impervious to any sort of defense - there's no way to see them in the sky with radar - and so I don't think there's any doubt about that.
It seems a little odd he says he announced it, when by more detailed accounts it was Harold Brown, his secretary of defence, who did it, on Aug 22, 1980. Carter probably meant his administration by "I".
Anyway, in the interview Carter says something that's reasonably close to "invisible by radar", so not just "invisible". For what it's worth, the press coverage at the time of disclosure used similar terminology, such as "radar-invisible plane" (Washington Post headline) or "virtually invisible aircraft" in the Armed Forces Journal. The more official term "Stealth" was also employed both by Carter (in the above snippet) and by the press of the time.
The 1980 disclosure created a political scandal at the time, after Reagan (and others) attacked it. Carter was forced to defend Brown's disclosure in a letter to Congress, so in this sense Carter did get more personally involved.
Another interesting twist is that (as DavePhD discovered) the congressional investigation into the leaks concluded that the aforementiond Armed Forces Journal article was pushed through and partly conveived by undersectrary William Perry in collaboration with the Journal's editor, who had already obtained a lot of relevant information from unclassfied sources, but had delayed publishing them at Perry's request. The Journal article was published on purpose just before Brown's press conference (and in fact mentions the imminence of Brown's announcement).
