SFO-LAX-LIM-CUZ (DL/LA/LA)

I've found multiple places on the Internet (for what that's worth -- none recent) which say that in Lima I'll have to collect my bags, get through customs, then go back to the front of the airport to get in line and check in again with LATAM and drop my bags, then go through security and get to my plane. The connection time is only 1.5 hours.

Then I called LATAM and they insisted that, if the connection time is under 3 hours, there's no problem, the bags will be checked through, just go to the plane. The rep even put me on hold to confirm.

Most websites don't even address how connections work at Lima. Has anyone actually done this lately and can tell me the reality?

Thank you!
-- Ethan