Have they actually been right with dates for their videos?
These "Old School" clips have been referring to them by decade as opposed to year.
I think Sesame Workshop is usually right when a date is applied to a clip, based on what I know. Timelines, Hulu, Old School DVD chapter stops, dates in the Sesame Street Unpaved special. But there are times that are provably wrong.
One of the most common date incorrections is the season two version of Rubber Duckie, the classic one that uses the blue background. Nearly everything that cites a date or season, whether it be Hulu, Old School Vol. 1, 40 Years of Sunny Days, or anything else, lists it as being from the first season, when we know that the first season version is different (due to things like Ernie's nose color and the fact that they didn't use a plain blue background in the first season).
Other notable things that have been incorrect: Old School Vol. 3 includes "Henson Ball High Wire" under season 15 classic cuts, when the segment debuted in season two and the alternate ending premiered in season six (and that version had already been included in volume 2). The timeline section of The Street We Live On has a few incorrections, such as showing a C3PO and R2D2 clip as being from season 10 (the episodes are actually from season 11), and showing a clip with Olivia listed as season six (when it's widely sourced that she debuted in season 8).
One thing I wonder about is Teeny Little Super Guy. The timeline in The Street We Live On includes the opening as a 1982 clip, and Old School Vol. 3 has it as a season 14 clip, but there was a press release for the 15th season that listed it as new. I'm not sure whether those clips all came from the same season or if they produced them over the course of a few. Maybe the first one was made in season 14 and then they made more on a regular basis in season 15.
I also wonder about "Kermit and the Weather Salesman" being listed under "season 7 classic cuts" in Old School Volume 7. Kermit and Grover look more like they did in seasons 3-4, and the video quality makes it look like a pre-season 5 segment (in the first four seasons, the video quality kind of looks like it was shot on film, while in season 5 it looks more video and less "film"). Could it be a mistake? Could the segment have been made a few years sooner but didn't air until season 7? Could it have actually been taped in season 7 (maybe using older puppets and the older video quality that was used in the past)? Could they have looked at the Muppet Wiki EKA, which was a season 7 episode (it's known that Sesame Workshop does use Muppet Wiki for research, but they should also use their own documents for final verification on these kinds of things... I wondered if that might have been the cause of the mistake for the Ball High Wire being listed as season 15, except Muppet Wiki already had a season 2 episode as the earliest known appearance)? We may never know (or maybe we will).
But whenever Sesame Workshop or whatever official cite lists a season, I usually believe it as correct.