Do you have a lot of experience in RF work? Sometimes these concepts are not easy to explain in a post like this. I am not sure your described methodology of connecting the router’s antenna connection to the core’s antenna connection is a good one since you are no longer terminating the output impedance of the transmitter correctly. The value you get could be higher or lower depending on a lot of factors, but it pretty much can never be correct.
The TI CC3000 returns its RSSI measurement in dBm, that is dB relative to 1 mW, so 0 dBm would represent 1mW of RF power. That would be a lot of power for a receiver input to see and I am sure the TI part’s RF input is not designed for 0 dBm inputs.
Checking the TI part datasheet, on page 6 it lists the maximum input signal level as -10 dBm in 802.11b mode and -20 dBm in 802.11g mode. It also shows the receiver sensitivity in dBm for the various modulation schemes ranging from -75 to -97.5 dBm which represents the minimum signal value needed on the input to properly demodulate the incoming signal.
On the same page you can see the typical transmit power levels ranging from +18.3 to +14 dBm so if you were to reattempt your setup with the router and you did properly terminate the output impedance, you would surely be swamping the RF input on the TI part by several orders of magnitude. Usually in this kind of testing you use either a fixed or variable attenuator to reduce the signal level.
A quick look at the free space path loss for 2.4GHz shows that you are looking at around 60 dB path loss at 20 meters, so it not unreasonable for the receiver to expect signals in the -40 dBm range.
I think if you had a good test rig with an RF signal generator and proper power levels, you might be able to get the core to show -10 dBm or -20 dBm RSSI levels that are the specified maximum allowable input, but even then I would not bet on it. I think the RSSI measurement is designed for over-the-air attenuated signals and while it is not spec’ed that I could find, they might have designed it for the normally low levels seen at such inputs.
I am also certain that the absolute accuracy of the RSSI value returned is not guaranteed, since I know that measuring received power in chips is hard. The ratiometric differences between return values is likely to be fairly accurate so you can say that a value of -50 dBm is about 10 dBm stronger than -60 dBm.
I think that if you really want to know the limitations of the core’s RSSI values, you will have to borrow some RF test equipment and test it since no one else is counting on using this data in a precise way.