At LAX there isn't an airside transit facility for international arrivals, you have no choice but to go landside -- effectively leaving the airport. So you are in the clear, and there is no problem with this "transit" giving you a half-day tour of LA. If they ask, you can always say you got lost going from TBIT to T4 and it took you a while to find the check-in. I'm certain you won't have any problems.