Problem powering OpenLog on Mega 2560

Yes, that's what I meant by "burst of data comes through". In the mininalist version, I only connect Vcc, GND and Rx on the OpenLog. When sending data on the Rx, there is always a noticeable downwards fluctuation in the voltage (I measure across Vcc and GND) no matter where GND is connected. However, if it's connected to the Mega's ground, the blue LED flashes and the data actually gets written, whereas if I have it connected to a generic pin set to OUTPUT/LOW, no data gets written.