All true except when coming in off a red-eye from HI and trying to connect to the 6am LAX-SEA. IIRC, the shuttle does not begin operating until 6am or so. This means you will have to exit T4 and re-clear security at T3.
Originally Posted by nako
No, you don't have to reclear security at LAX. In Terminal 4, go to Gate 44 - the Eagle shuttle - and show them boarding passes (or an itinerary) indicating that you need to go to Terminal 3. You'll transfer at the Eagle terminal to another shuttle, which will take you to T3.
The last few times I've done this, the entire trip has taken less than 20 minutes.
Mike