1) with EyeTV Receiver > Apple Remote disabled (= ignore all input 
from this source): no IR signal is received 
2) with EyeTV Receiver > Apple Remote enabled (= use all input from 
this source): IR signal is received and reacted to

If the signal would have been received by the built-in Apple IR 
receiver, it'd also be received in case 1) and in all the other cases 
that Apple's support has also mentioned (prior to OS X boot, by the 
EFI firmware's boot menu, etc). But it isn't.

Best regards, 
Felix Schwarz