Any leads or wires on the scanner would likely affect some characteristics, like adding a groundplane to it. RSSI wouldn't necessarily indicate the amount of reduction in quiescent noise floor unless that's what you guys are measuring. If so, then carry on. I missed it.
Otherwise, what I would have done is generate a UHF signal with a service monitor using the scanner's antenna and lower the attenuator until I have a quantifiably noisy level (I'd try to jack into the audio circuit for a 12 dB SINAD measurement, but the leads might affect the test). Then I'd do the tape hookie-dookie and look for the delta between no tape and tape. If I can lower the signal level on the attenuator and get the same result in noise, then I'd declare great success. Otherwise, the more thingies attached to the radio, the better the possibility of changing some of its characteristics.
And, we have the possibility that it's not shielding that's making the difference, it's adding more of a groundplane surface. Maybe?
Wow, I haven't had this much fun on here in a long time!
