sure it does, i run into this all the time with time warner or comcast set top boxes. technically, your 4:3 tv show is still being ouput at 720p (at least it is upconverted to that format) the same as the movies... unless your box has the option of outputting "native" in which case it does exactly as you describe. if you have an LCD, you are immune from "burn in" in the traditional sense of CRTs and plasmas. you can get a ghosting effect or a temporary burn in that is not permanent, but nothing to worry about. if you have plasma, then yes, you do have to worry about permanent burn, even though newer models have improved over some earlier models.
i can value the cable boxes ability to adjust aspect, and often times i take advantage of it (i am an automation systems programmer for control systems). but in the systems that i program, i have the luxury of communicating with the HD display and setting them to the correct aspect ratios and the end user does not have to think about this. i just note that in instances where consumers do not have the luxury of full automated control, they will more often than not at some point "mess up" the aspect ratios where they are in some twilight zone weird in-between mode. both approaches have their merits. but lets talk about DVD players... they don't have aspect ratio controls, even the progressive players that output 480p... just an aspect ration setup in the settings menu, same with XBOX360 and PS3? (not sure).
some day, this will all be a non-issue once everything has transitioned over to 16:9. on split decisions like this, it is pretty predictable that apple would take the road with less complexity. maybe we will see a more full featured remote as an option in the future for those that want to transcend above the front row experience?