Also - note the context of the two questions you referenced are different. One person wanted to scale the same video over multiple pages and get rich snippets for all those pages - This is doable but inadvisable.

The other context was someone asking if they can upload the same piece of content to two hosting platforms - which i generally don't advise as you can cannibalize your rankings.

Not entirely true. They do have the ability to pull out data from an encapsulated video file and work out where content is indentical. This isn't an issue, like you say, if the pages are different in other ways. But, Google can recognise when videos are unique vs duplicated

There isn't an issue with having the same video on two different pages, but there is an issue with uploading the same video twice and behaving as if it were different videos.

In your situation, I would recommend only having an XML video sitemap entry for the page where you want the rich snippet. Embedding the same video on two pages is not a problem