Here is the photo cropped for better viewing. Apologies to Paul for cutting him out so severely. In the original shot he's the guy standing on the right. We have no idea what song they are working on at the time this photo was shot
Chet is holding the fancy Martin and Jerry is holding a dark sided guitar with classical rollers on its tuners. This is one of those shots you almost can "see what you want it to be" but I'm not seeing a classical light wood top on Jerry's guitar. It makes sense Jerry would have an Ovation on hand but it also makes sense that Chet would have brought along his DV. They probably agreed on it being an acoustic recording so Chet would naturally bring the DV "just in case"
In the "see what you want to see" category I see the hint of a DV ring hole on the top upper bout on the guitar Jerry is holding and as I suggested earlier, that doesn't look like a blond top classical even though it has classical looking tuners
By now I have listened to to the clip of ISYIMD probably twenty times since it first got posted and here is my addendum.
1. When Merle starts playing the song I think Jerry is the one doing the rolling rhythm backup. It sounds more like him than it sounds like Chet. Chet would have sounded a little smoother I think.
2. When Chet actually takes his solos I'm still not hearing "Martin" but something else. When he plays mid range to high melody notes I'm hearing either the DV or some other acoustic (possibly the Ovation) that delivers an enhanced, edgier tone to single notes in the mid to high range. (edit: the opening notes in Chet's second pass in particular sound DV)
so I flip-flop back to calling it a DV
3. Musicians at that level, in that kind of session, think nothing of switching guitars around to keep things interesting and not having the faintest idea that people like us would beat on the "who/what/when: for days.