It happens also when my character is right next to her owner, and neither one standing still. What I understood from the post I linked, and what seems plausible to me here as well, is that there is a conflict between different stand animations, where SD+ wants the character to be on all fours, while ZAZ animation pack wants her to stand with her wrist tied behind her back, because she's wearing wrist chains. And apparently then removing the wrist chains solves it for them, sadly that doesn't solve it for my game.
I was under the assumption that there is no actual crawl animation btw. When I move her while she is in a crawl position, she comes back to her feet, with hands tied behind back and then walks, and when she stops moving, she goes back on all fours. (as long as she's close to her owner, of course)