Definitely some resource guarding. Stella did this recently when I gave her a duck foot. Whenever I was near her, she'd turn her body away, she tensed when I touched her, and actually growled when I put my hand on the chew.
What I did was grabbed a different high value treat, then while she was chewing, I said "drop it" while holding the new treat near her nose. While she was eating the other treat, she really didn't care that I was taking the duck foot away. Then I'd repeat - I gave it back to her, then asked her to drop it again. Now I can say it from across the room and she'll actually drop whatever she's doing and come over to me.
I hope this helps you!