If the rentals are stored as they are when you Handbrake your own video, there are NO BLACK BARS in the video file itself. Try playing a "black barred" video back in a software screen (like Quick Time player). Because QT can make the window width & height whatever it wants to match the video OAR, there are no black bars- just edge-to-edge video. The only exception is when someone has chosen to encode something that does have the black bars burned into the file (but even there, Handbrake is pretty good at cropping those off).
When the file is displayed in a hardware-driven width & height window (your HDTV), the black bars are created to maintain the OAR. If the full width of the video is too wide for the fixed width screen, black bars will be created at the top & bottom so that the full width just fits into the hard-limited width available on your screen. If the video is too tall for your HDTV, black bars will be created on the left & right so that the full height of the video just fits the hard-limited height of your screen. The goal of this approach is always the same: to show as much of the picture as possible, layering in black bars where needed to do so.
Key is not confusing the concept. The video companies do not plot to burn blank back bars into video files to limit the height or width of what is actually shown on the screen. Instead, they see their creations as a work of art, and generally assume that their market wants the full work of art, not a version that has the left & right (and/or top & bottom) cut off and/or distorted via stretching techniques to make it fit a hard-limited screen of 16:9 or 4:3.
As is right now, there are more 4:3 screens in the world than 16:9 screens. If they were rendering ONE version to satisfy the most TV owners, it would be the old "square" shape typical of SD television. Those of us with 16:9 screens would get black bars on the sides.
If they rendered for 16:9 screens, those with 4:3 screens would get black bars on the top & bottom.
If they choose original aspect ratio (OAR), they deliver the full width & height without distortions as the director & producer envisioned it. Sometimes that is 4:3. Sometimes that is 16:9. Sometimes that is more than 16:9. When the OAR differs from the fixed dimensions of your HDTV, the black bars mean you are getting to see the WHOLE, non-distorted picture, as originally intended. Some directors frame their shots so that important stuff happens in the fringe (edges). When you use tools to auto-crop (to fit), you won't even see that stuff.
If you go to the cinema, they typically duplicate the software-version of video playback by adjusting curtain width & height to dynamically adjust the shape of the screen to match up with the height & width of the movie you've come to see. Instead of black bars, the curtain arrangement properly frames the playback screen, but the end result is exactly the same: show you the video exactly as it was intended to be seen. Black bars on our TV screens is the "lazy" way to do exactly the same thing (the black bars are our "digital curtains").
The OP has a relatively small screen. I can certainly appreciate the desire to watch rentals/purchases in bigger sizes, especially when the OAR is very wide screen. I recall having a 35" screen many years ago, and some OAR would show as only about 1/3rd of the screen height- a wide strip of video sandwiched between almost as big black bars at the top & bottom. It could make you wonder if something was wrong with the set if you didn't understand OAR.
If your (OP) screen is 4:3, you might want to key on the SD versions of iTunes rentals, though most modern programming has moved on to 16:9 as standard. If your 32" screen is 4:3, you might want to consider selling it and getting a 16:9 set, which will be "full" with the vast majority of TV (and many movies) shot these days.
If your HDTV is already 16:9, I'm not aware of any (major) TV shows that are being shot at anything wider than 16:9, so any TV shot in HD should be filling your screen (SD video will put black bars on the sides to maintain 4:3, but SD as a standard is fading fast). If you are watching old 4:3 SD videos, you only get to "fill" the screen by stretching them out wider (making everything in the video "fatter", or by distorting the far left & right by putting most of the stretch toward the edges and less in the center). Either way, 4:3 won't look great stretched out to fill a 16:9 screen.
If the issue is mostly movies (on your 16:9 screen), movies are still shot in all kinds of aspect ratios, as they will have no problem playing back on the flexible width & height arrangements of cinema screens. Best options are:
- since your TV apparently won't let you adjust video received from the Apple TV, try pushing the video through a receiver that will let you zoom in to fill the screen (you're losing picture but you don't seem to care about that)
- try the stretch option (with the receiver, you're not losing picture but you are distorting the picture, making actors taller & skinnier when using this to get rid of the black bars on top & bottom; the actors might like you doing this)
- get a 16:9 HDTV if you are still using a 4:3 HDTV (most everything is moving away from shooting in 4:3)
- buy a bigger TV. A hop to only about 42"+ would likely deliver the same maximum height of video you are seeing on a "full" 32" screen even when dealing with a very wide OAR (Lawrence of Arabia, etc). 42+" HDTVs are increasingly cheap these days, and should be even cheaper into the holiday season. Used ones- even fairly recent models- seem like they are being given away on sites like craigslist.
- sit closer to your 32" screen when you watch letterboxed video; that way you get to see the whole picture as intended
Again, that last one is "learn to love OAR". The analogy that I might offer is the private collector who manages to buy the Mona Lisa or similar, but then finds it to be just a bit too big to fit the intended space on his/her wall. Do you really think the best option is to cut off the edges of the painting to fit the space? I know that there are hardly any movies to rank up their with something like the Mona Lisa, but the bulk of the creative side of the entire motion picture industry thinks about their products that way.