You are correct. The frequency overlap is not an issue post bbc. The issue post bbc is how far you can separate the bbc from the receiver.
The intermediate frequency (output of the dish to the bbc) is 250 to 750 MHz. The bbc up-converts that beyond the ota range.
OK that's what I suspected. So it's twofold:
1) Signal loss due to the fact that the BBC output is a much higher frequency, leading to increased loss per foot of coax...
2) BBC signaling failure due to "signaling" voltage or signal loss/corruption due to distance... the "signaling" being the control signals being sent from the receiver to the BBC.