I made that comment as a supposition based on the layouts of today's airports. Today, because of elevated jetways directly to planes from concourses, departures are on the second level and arrivals are routed down to the street level for baggage claim.
Back then, when you had to walk out to the tarmac to use external stairs to board a plane, departures were on the ground level, and baggage claim may have been in another building entirely. I've even been in old regional airports where baggage claim was a rack in the corner of the tarmac where baggage handlers would just put bags on a multi-shelf rack for customers to pick up.
I was browsing through the other photos at this site, even looking at photos from the 1950's and 1970's for clues to the inside of the ticket lobbies. There are a few dedication photos that show a corner of an inside, with an angled ceiling that doesn't look like the wide-open high-ceiling of the photo of the 1960 old terminal (which looks like the same counters as in the Obama photo).
-PJ
1965 (15 Sept)
Demolition of the old terminal building at HNL was completed.
The picture of Obama and his dad could not have taken place inside the old terminal building in 1971.
There was a rather large hurricane that hit HI ... 2 years ago? We got a check-in from a bunch of HI freepers.