Your thinking is right, the statement is half baked.
HDTV's can be RPTV, FPTV or direct view, just like regular TV's. The similarity ends there, as HDTV's are capable of much higher resolution that standard TV's can not display.
Standard TV resolution is defined as 480i SDTV. In addition, an HDTV (High Definition) is capable of either or both 720p and 1080i. Almost all HDTV's are also capable of 480p EDTV (Enhanced Definition).
Some current X-Box games can produce a 480p EDTV output, which is significantly better than 480i SDTV.
Future X-Box games are slated for 1080i output which is native HDTV, about 6 times the picture information than SDTV.
It is true that an X-Box or HDTV stb can be set to downconvert higher outputs (480p, 720p, 1080i) to 480i. But it would not be EDTV or HDTV, it would only be SDTV.
To take advantage of the the increased resolution of EDTV or HDTV, from X-Box or a stb, you must have an EDTV or HDTV. It's as simple as that.
As far as damaging an HDTV, if you have the set properly adjusted, and do not let fixed graphic images stay on the screen for indefinate periods of time, you should be fine.
And the bigger the HDTV, the more immersive the gaming experience. Immersive = more realistic.
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