Wow -- thanks for all the comments, folks, I must have struck a nerve! I'll try to respond to all of them here, in sequence:
John Galt: I loved your comment about "no user serviceable parts inside"! It was echoed by etresoft, too, later in the chain; sounds like good advice if this ever happens again. You mentioned that Yosemite incorporated a lot of changes to TM, but I'm not using Yosemite (have been avoiding this upgrade, as it sounds too buggy). But apparently your advice holds with Mavericks, too.
Etresoft (3:17am): very good point -- I think that's exactly what I did. What I'm still not clear on is: are the backup files themselves (ie the actual data being backed up, as opposed to hard links) stored in the backup folder that TM creates, or are they kept in a separate file or folder? It sounds like it's the former, as I had originally thought. But pondini led me to believe that, if the data WAS stored in the folder, it would not be deleted if there were any links to it in future backup folders. From what you said, I'm thinking that's probably true IF you are dealing with a backup that's INSIDE TM, but not if its a folder OUTSIDE TM. Is that right? If so, this really is a pit that's ripe for idiots like me to fall into.
Lex Schellings (3:52am): I don't think I understand your comment -- you said "All these instructions are to delete a specific file... You should never deleted a dated FOLDER". But instruction #2 says "One or more individual backups -- it's best to use Time Machine, per the green box below" -- then, in the green box, it says " Locate the backup or item you want to delete via the Timeline or "cascade" of Finder windows". Since I was trying to delete a "backup", what was I supposed to select, if not a folder?
Etresoft (4:15am): that's an interesting thought, but I don't think I used the sidebar to navigate to the backup I deleted. When I opened TM, it showed me a sequence of Finder windows with the Star Wars background, but the external hard drive in the Finder window was grayed out and inaccessible. So I checked pondini again, and it said I could get to it by right-clicking on the TM icon in the task bar (after exiting TM), selecting 'Browse other TM Disks', and selecting the one I wanted. After I did that, I could see the external hard drive in TM was not gray anymore, and I navigated to the first backup folder. Apparently, that's what took me "outside" of TM, even though I thought I was inside it. I will definitely follow up on your suggestion to go to Apple's bug report site and file a report; thanks!
Lex Schellings (4:39am; do you guys ever sleep?): I didn't hear that pondini had died -- I hope you folks weren't close to him; sounds like he was very thorough, and trying to do the right thing. He just didn't realize there were people like me out there.
I'm surprised at your comment that "the behaviour of deleting one of the TimeMachine dated folders in Finder has always been the wrong way, leading to unhappiness." That is exactly what our tech support department (which is run by Lockheed Martin; they're supposed to know what they're doing -- at least they certainly charge JPL enough for their service) said was the approved way to delete old TM backups, and in several cases in the past, it has worked for me. In any event, I didn't think I was deleting the TM dated folder through Finder -- I thought I was doing it through TM, as pondini recommended. Silly me.
Etresoft (5:24am): It's a little scary that you said "I don't know of anyone who knows Time Machine well enough to actually update it." Were you joking? I definitely agree with your (and John Galt's) advice that "I wouldn't recommend any kind of interference with Time Machine, especially with the Finder". In the future, I think I will just set up a separate partition on my external drive for TM backups, and let TM figure out how to thin itself out.
Lex Schellings (5:43am): "a magic black box" -- that's a very good take-away from this misadventure. Thanks for your advice.