I talked to the Apple advisor earlier today, and she said, based on the info the AppleCare advisor sent them when troubleshooting with me (and they claim this is the first they were aware of it--apparently they don't read their forums thoroughly), that there is a problem with activation or recognition of the Media Source Extensions (MSE) part of HTML5, which is what I had come to suspect, with Safari 9 and OS X 10.9 (Mavericks), but not with OS X 10.7 (Lion), 10.8 (Mountain Lion), 10.10 (Yosemite), or 10.11 (El Capitan), only OS X 10.9. She said Apple is working on a solution which will be corrected in a future update (not the one that was released yesterday) but she could not tell me what time the schedule would be. I have no idea why only Mavericks is affected. She said they were working with YouTube to solve the problem, but I don't think it is strictly a YouTube problem because when the first AppleCare advisor tested my system with a 1080p animation video, which he knew to be 1080p, generated from the Apple store, Safari 9 still had the same problem of no 1080p.