Lol! I think basically they like to sit in their favourite place to snack. If you had a nightcam you might see what she gets up to, but I would guess, having seen our Syrian's night time habits. That she does a lot of wheel running before she moves everything into the wheel. And then loves it so much she wants to snack there. Our syrian's night time habits are. Foraging for food and in the food bowl after lights out - taking that back to the nest. Then running in the wheel for a long time. Interspersed with going to a favourite place for grooming. Running. grooming, running grooming. Then around 3am - more foraging and snacking. That might be the time she decides to snack in her wheel
But just guessing. I also wonder what she'd do if you just left the things in the wheel! Maybe it's become a game! They do things like that. The Silent runner is quite enclosed so a nice place to sit and snack.
I'd try just leaving the stuff in the wheel for a few days. See if it's still there in the morning. If she can't run in the wheel she'll probably drag the chew out again. And get the message!
If that doesn't work, then as Ria says, swap the wheels over. But I suspect it's more to do with cage habits than wheels.
It could be a couple of other things too. If she's worried about her hoard being "stolen" (ie if you remove it or spot clean it) then she's trying to keep her favourite stashes safe. Or if you clean the wheel out rather a lot? To claim it by eating there or something?