There are two different places that the "factory" keyless entry can be installed on the Corolla. The first is at the assembly plant. With this installation you get 2 master keys with the remote built into the key itself with the remote trunk release. There are VERY few Corolla LE models that are being produced with this option.
The second place the "factory" keyless can be installed is at "port" or the dealership. This is still the Toyota "factory" system, but it only has the remote lock and unlock and not the trunk release as that system can only be done during asembly of the vehicle. ("port" is the central distibution location for each region where vehicles are shipped from the assembly plants to be distributed to individual dealerships. This is where many accessories (factory installed, but with Toyota, they are called "port installed" are installed)
From what you are describing, you do have the "factory" remote keyless entry, just didn't get one that was built on the assembly line with the vehicle. (From what I've seen so far this year, Toyota has been producing less than 5% of the LE model Corolla's with the keyless built from the assembly plant)
Hope this helps.
Ken
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