I never really understood the meaning of the term "exoskeleton" with respect to car manufacture anyway. I think it's a term that should be reserved for arthropods and Ironman.
The interpretation of Musk's claims has largely been that he was describing
monocoque construction. This is where the skin of the object supports the loads such as in airplane wings, rockets, and egg shells.
What it very much appears more traditional 'unibody' design. Now unibody is often referred to as a type of monocoque and it sort of is to a small degree. In unibody, the parts of the vehicle that weigh the most, the power train/engine, are mounted to the same frame that the skin is attached to. This is where semantics and terms of art can really start to blur things, because the 'body' of say a car, usually
is not the 'skin' or 'body
panels' when talking about construction of a car. However, the terms 'body work' and 'body' to the general public and in everyday conversation even among mechanics usually means the
panels, and not the body that the body panels are mounted to. Sometimes some of the body panels
are part of the the body and structural. This is most often seen with the roof but also the rear pillars. You know those rear pillars on the various Prius that are kind of wide? They're part of the body (or they were when I toured the Aichi plant a decade ago). That is closer to a 'monocoque' build, but because the panels that are structural are so few compared to those that aren't, it's still generally considered a kind of 'unibody'.
'Body on frame' is a slightly heavier and older construction method where the powertrain is mounted to it's own frame, the chassis, on which the frame for the body panels are still mounted. It's still the common method for most full sized trucks. My Silverado has some body panels that are in need of replacing from rust, but I could literally take them
and the sub frame they're on off and the vehicle would still work, assuming the frame I took off was not the one holding the steering suit and seats. Some cars are a combination with sub frames. My old Subaru had a rear sub frame that kind of worked as a chassis but not for the power train which would have made getting the gas tank out to find the minuscule leak a pain. 'Luckily' I blew the engine first.
Basically the more separate 'frames/bodies/chassis' you're attaching together and the less it uses the panels for structure, the more 'body on frame' it is, the fewer differences in them leads into 'unibody', and the more the panels or 'skin' is used structurally the more of a 'monocuque' it is.
It very much appears that the Cybertruck is mostly a unibody with
one structural panel making it
less of an 'exoskeleton' than a decade old Prius.
EDIT: To be clear,
the accusation being floated is that instead of the thing they have been calling 'structural skin' being part of the structure, it's just an unusually large body panel, which only makes the vehicle more difficult to repair and maybe some other drawbacks, but is not actually being used structurally. The drive train chassis seems independent of it.