While I think that everyone has some logically sound theories regarding the cause of this behavior in the various threads I've read lately, I don't think it is that rare, and don't think anyone is correct, either. While new to Panther ownership, I have extensive experience with reptiles in general. I have never seen this behavior in any other reptiles I've ever kept, but noticed it immediately with both my male Panthers.
The most plausible answer, biologically speaking, may be compensation for some perceived/real nutritional deficiency, but my chams eat a varied diet and always have, so not likely in my case. Obviously their diet is not identical to what they'd eat in the wild, but there is enough variety of vitamins/minerals to negate that theory. Additionally, if you could see the gusto with which they'd sometimes go after a small piece of bark or tip of a stick, I think you'd agree that this is not a subtle behavior.
Regarding lack of moisture/humidity/drinkable water, that is not reasonable either as they always have plenty of access to water in various forms, and have both even been seen drinking directly from small water bowls.
I will say that they only did this on real sticks/twigs that i gathered from the back yard for their cages - I have a few different types of artificial vines and they've never been observed trying to eat them whatsoever.
This would make an interesting behavior for future study to be sure.