Duplicate RX in uart (two devices listening one of which is data-logging)
You may be misinterpreting a part of that page. If you look for the text "It can be safe to connect multiple receiving devices to a single transmitting device" the diagram shows a way to connect the two that should be OK for this case:



A few of the warnings on the page like "you can’t pick and choose which device hears what transmission" don't really apply in your case because you do want both devices to hear all communication from the device. 

A big no-no with serial communications is attempting to connect two transmit lines together, but generally feeding a transmit line to several receivers is fine as long as you pay attention to voltage levels to make sure they're within range for your microcontroller and for example don't try to connect RS232 levels to a TTL device.