Cliff it seems to be working for me with my iPad the way I have always done it...
Yes, the "share" option, in most cases, should work fine, provided the share option is available for that video, on your device, and fully supported (requires syncing for some devices/software).
What's not working the way it should (and causing issues with some links) is the forum's video embedding plugin. How it USED to work is whenever someone posted a link to the video's page, the plugin automatically parsed the link and embedded the video. That part is no longer functioning as it should, due to changes/updates. The plugin is simply sorely outdated.
Again this is something I was already aware of because it's been happening for a while now. We have some other updates planned, BUT it will require temporarily taking the forum offline, which is why it's low priority (there's more behind the scenes stuff that happens to keep the forum up and running than most people realize).
In the mean time, if YouTube's "Share" option is available, people can use it post (and embed) videos. But even that is not 100% guaranteed until I get the plugin updated.
Hope this makes better sense.