Whoever said that most movies are anamorphic was incorrect.
There seems to be some confusion here about what an anamorphic format is. It certainly is not "any format with letterbox bars" when viewed on a 16:9 TV.
The most common format in film today is Super 35mm with a spherical lens. This format's native aspect ratio is actually 1.37:1, close to 4:3. But the image is soft-matted during projection to an aspect ratio of 1.85:1.
The only true anamorphic format in common use today is Panavision. Contrary to popular opinion this is not 2.35:1 aspect. 2.35:1 is the aspect ratio used by early Panavision cameras and lenses, and more particularly in the defunct CinemaScope format. Panavision is a 2.39:1 aspect ratio (frequently rounded off to 2.4:1), and it is only force of habit that the industry itself often mistakenly refers to it as 2.35:1.
The anamorphic lens is aspherical, and has a different compression horizontally than vertically. What's more, Panavision improves upon the CinemaScope format by varying its optical compression gradually from the edge to the center and by use of dual rotating elements that adjust the anamorphic power proportional to the depth of focus (DOF). It was the case with CinemaScope that the anamorphic compression in closeups (for obvious reasons).
Unlike 1.85:1, in which the image is matted in the projection room, 2.39:1 Panavision consists of a wide image that is optically squeezed onto a 1.37:1 frame. This is reversed in the theater, but this is different from anamorphic compression on DVD.
The confusion over anamorphic formats is doubled by the different use of the term where DVD encoding is concerned. Similar to the Panavision concept, the image undergoes compression but in a different direction. Whereas Panavision horizontally compresses the image during filming, and expands it horizontally on playback, DV NTSC maintains a 720x480 resolution that is vertically compressed for widescreen playback, whether on a 4:3 or 16:9 TV.
If a source is 1.85:1, a hard matte is added during encoding to conform 1.85:1 to a vertically taller 1.78:1 (16:9) frame. If a source is 2.39:1, a thicker hard matte is applied during encoding to conform Panavision to a 16:9 frame. This happens regardless of whether the TV is 4:3 or 16:9. The image is encoded vertically stretched on the 1.33:1 DV NTSC (720x480) frame, and then vertically squeezed by the DVD player to fit within a 16:9 frame. If the TV is 4:3, then additional matte bars are added by the DVD player to output the 16:9 frame within a 4:3 display.
That being said, AppleTV has a bit different methodology because it can downscale and upscale, supporting various resolutions unlike a non-upscaling DVD player. But in addition, H.264 is a format that is designed for multiple applications including computers. Computers generally stick to square pixels, whereas ATSC (HD) and NTSC (SD) use nonsquare pixels. So, inherent to encoders like Handbrake is the ability to carry two output resolutions in a single file... e.g. 720x480 for nonsquare pixel displays, where the pixel aspect is altered to conform 720 x 480 to a 16:9 frame. 853x480 is the output resolution one would use to output to 1.78:1 if feeding through a device like AppleTV that uses square pixels.