Yes. It was on a VHS tape that recorded it in 1988. I remember seeing it on the tape in the 1990's which is why I how I remember it.
It's amazing that there are records of when it aired. Why wasn't it shown more times in the 1980's? Was it because Mr. Rogers was making lots of new shows then?
If you look at the home page of this forum, there is a link to broadcast schedules going back to January 1984. The Dec. 30, 1982 date was just an estimate, since the printed schedules don't go back that far. I've asked Tim a few times if he can get earlier schedules, but I'm assuming he hasn't found anything so far.
As for how the schedules worked back then: they would air all of the post-75s every year, and then fill the rest of the year with pre-79s. So each post-75 week would air more than the pre-79 weeks, and the pre-79 weeks would air less and less often as more post-75s filled the schedule. Also, in 1983-84, only part of the 1969 season aired, and then starting in 1986, only the 1970 and later seasons aired.
As for specifically 1291-1295: what happened there was, in 1991, they ended with 1290. Then in 1992, they jumped all the way to 1351, skipping all of 1291-1350, none of which would ever air again. That is why 1291-1295 had its last airing so early.
Also, my estimated Dec. 27-31, 1982 date for 1291-1295 was not the first airing of that week during the 80s, just the first time it aired during your lifetime if you were born in 1981.