pixelated during fast action

Hello all,

Well my grandfather came to my house last year and watched the Superbowl on
my Sony HD RPTV. He loved it and wanted one of his own. I steered him
towards a Mitsubishi DLP. He just got it and I set everything up with his
DVD/Cable, etc... I stopped by lastnight to see how the football games
looked in HD on his set as compared to mine. During the game, as long as
there wasn't much action, and the camera was relatively still, the picture
looked great. However as soon as the camera started to move with any amount
of speed (to follow the players) the picture would go to crap. It would
become very pixelated. As soon as the action would slow back down the
picture would immediately improve. His Mitsubishi has a built in HD tuner
and I currently have component cables running from the cable box into the
component inputs on his TV. I set the cable box to bypass it's own HD tuner
and use that of the TV's. I live very close so I went down to my house to
see if the same was occurring on my TV. Nope, even when the action sped up
the picture remained perfect on my TV.

Some things I was thinking:

1. Maybe the HDMI cable would fix this (hdmi from his cable box to his TV)
2. Maybe this is just the way it is as the broadcast is in 1080i and his TV
is native 720p (my TV is native 1080i)
3. The cable company is just screwing up the broadcast somehow (he receives
his local HD's through the cable, not via an external antenna)

Any ideas on what might be causing this ?