Rebroadcasting taped programming isn't anything new for The Weather Channel. Even in the 1980s, the overnight hours were the same one or two hours replayed again a couple of times. (That's what led to the infamous double-long long-format local forecasts while TWC rewound the videotape!)
However, packaging rebroadcasts as "live"... that's just not kosher. If the word "live" is in a program title, viewers expect it to actually be a live broadcast.
And I honestly didn't think about it before, since I've never been to the Pacific time zone, but you're right - viewers on the west coast get to see only prerecorded material for what should be TWC's biggest primetime weather program.