Assuming that the parent commenter is right and that they are using internal line cards, I wonder if the external modems were being added to support higher speeds.
However, the fact that we can see at least 2 (but I think four) 66 blocks means they had 50 to 100 phone lines for the machines visible, which would make sense that the external modems are the primary connection and no internal modems are being used, based on the number of modems visible and the fact that each 66 block can handle 25 lines.
So I would say that almost definitely, they are using 1 (or 2 for some on the right side of the photo) external modem per PC connected to the 66 block, those analog phone blocks tied back to the channel bank/multiplexer, and the carrier's T3 tied in there.
No internal modems used at all.
And the person who posted the photo on twitter is none other than Scott Miller, founder of Apogee Software, publisher of some of the most revolutionary games of the late 80's and early 90's, and this BBS (Software Creations) was the cornerstone of distributing the shareware versions of those games. Very cool bit of history, I remember dialing in to Software Creations to download Commander Keen!