The photos are a good illustration. Side photos don't really show much, but when looking at the front, you see where the issue is. Thin wood and not much of it.
I think that of all the American sidelock (or side plate) guns, the ones least likely to get stock head splits are the Lefevers. This being that since their design is technically a side plate box lock, there is more wood behind the action than the other makers.
Granted, they have their own issues, like those thin top fingers breaking and their wrists breaking.