You should be fine. I think Google is going to get smarter and smarter at recognizing the same video, but if it's relevant to the page and there is other supporting content, it is adding to the user experience and you'll be ok.
Another option to consider on certain videos is to create a 2nd video (in Wistia). Essentially it's the same upload, but a new file with unique title/description etc. YouTube doesn't let you do this, but you'll be fine in Wistia. This could come into play if there is the same video with a sightly different context that needs to be on 2 pages.
One question I'm pondering is the situation where a 'how to' video get's the attention of prominent bloggers. Let's say 15 big blogs in your industry all use the embed code (if you make it available) to post the video in a post of their own. This A) should benefit with by receiving a backlink, but B) does this complicate the waters from the Search Engine's perspective? I guess it's still on your video sitemap, and Google should know that you're the original source.
We just started on Wistia, after a few years on BrightCove and experience with a bunch of others. Pretty cool platform, plus I hear a new (and much more flexible) player is coming out in December. Exciting!