So, yes the VHS is expected to have more magenta.
Anecdotally, I remember watching Aladdin at the movie theatre when it came out and later on TV multiple times and the VHS you saw doesn't correspond to my memories at all.
I can't challenge the vividness of your memory. That's all in our heads. I remember it one way, and you remember it another.
The author is not wrong that oversaturation is a source transfer phenomena (which will always be different unless special care is taken to compare with the source material).
On most TVs that magenta wouldn't have shown as much as the youtube video shows because TVs tended to have weaker magentas. Of course, it's not like TVs were that uniformly calibrated back then and there were variations between TVs. So depending on the TV you had, it might have ended up having too much magenta but that would have usually been with more expensive and more accurate TVs.
TLDR: Transfers are hard, any link in the chain can be not properly calibrated, historically some people in charge of transferring from one source to another compensated for perceived weak links in the chain.
Regarding my memory, it becomes shakier the more I think about it. I do remember the purples but me having watched the cartoon could have affected that.