I just noticed that if I switch to "https://", Flash-based videos are now served. Back to "http://", same video served HTML5. So this is it, "https" is the culprit (for whatever reason)?
So, could it be that Firefox somehow doesn't provide the proper cookie value telling the site to use HTML5 when using "https://" (I did set HTML5 pref with "https://")?
Edit: A cookie named "GED_PLAYLIST_ACTIVITY", used for "[e]ncrypted connections only", is used on Firefox only. I don't see this cookie on Chromium on an encrypted connection. So, there might be a link with the presence of this cookie and the serving of Flash-based videos.
I can confirm this is the behavior I'm seeing on Firefox. However, it's important to note that YouTube seems to force https if you're logged in, meaning logged-in Firefox users ALWAYS get the Flash player. I've resolved this for now by installing the YouTube ALL HTML5 add-on ( https://addons.mozilla.org/en-US/firefox/addon/youtube-all-h... ).