Assume that was the pilot, as is the custom I believe. Other people who have more experience with civil aviation might be able to tell us.
In commercial aviation, there are at least two people in the cockpit, and two are pilots. (Flight engineers aren't needed in the current generation of commercial transport aircraft.) One of the two is the "pilot flying", the other is the "pilot monitoring". While I can't say it's a absolutely firm rule, the radio calls are handle by the pilot monitoring. That means one can say nothing definitive about the pilot who is actually handling the controls. The pilot flying can hear the traffic from ATC; he or she has the pilot monitoring actually do the talking -- most of the time.
I also remember watching stories about how LAX has, over the decades, been experimenting with additional ways to prevent runway incursions. The equivalent of railway crossing gates is not, um, practical. Most of the effort has been to improve ground radar, and installing what amounts to automatic traffic lights. :)
Thank you for that clarification. I was always under the impression that the pilot who was in the process of taxiing or flying was the one who spoke directly to avoid miscommunication (the telephone game).