Welcome to the Q&A Forum

Did you receive the answer you were looking for?  I'm going to go ahead and mark this question as "Answered," but if you need more info or help please let me know.  Thanks!

Wistia's sharing buttons still share the URL where the video is embedded, not the individual video - just like the buttons we have implemented.  We just don't want to have redundant sharing buttons all over the page, so we skip Wistia's sharing buttons in favor of the buttons already in our blog template.

Ben, you are absolutely on the money on this one (not surprised!).  Because our blog template automatically adds sharing buttons to each post, and videos are published within blog posts, using Wistia's sharing buttons on the videos themselves would create redundant sharing options on each page.

From an SEO perspective, there is no advantage to using buttons one way or the other - you simply need to consider factors like do you want users to share the video, or the entire URL?  From a UX standpoint you don't want to have sharing buttons all over the place, confusing people, which is why we're not using the Wistia sharing feature

Your site should not be affected by other sites hosted by the same provider.  Think about huge nationwide hosting sites like GoDaddy - if sharing hosting with websites with questionable content was a problem, a LOT of websites would have a problem!

I would leave keyword density out of it - go ahead and do press releases, but your goal should be media coverage, not link building/SEO.

I would say, don't use press release syndication as a way to build links - it tends to generate duplicate content an David's right, the links aren't worth much.  Instead, use PR the way PR is traditionally used - to build awareness and encourage media outlets to cover your stories in their own words.  The last thing you want is for your own content to outrank you on somebody else's site!