I have never looked into the exact details of the URC emitters and base stations, but if they include a series resistor in each emitter, this may create enough isolation between LED's to enable parallel connections. If there is a series resistor in each controller output, then the value and ratio between this resistor and any resistors included in the emitter become important.

Series resistors in the controller outputs attempt to protect from excessive external loads. Series resistors in the emitters protect the LED's from potential excessive current that may be available from the controller (depending on its output impedance).

Some of these little combiner/splitter boxes are a simple resistor/diode matrix, while others have separate drivers for each output.