Without giving Amazon too much of the benefit of the doubt here, I've noticed they love to offer you "coupons", generally with a midnight expiry.

I expect it's 100% a tactic to get you to commit to something you've looked at a couple of times but might be on the fence about buying.

I get the same as OP's logged-out price (nothing hidden) while logged in, perhaps if they are offering a coupon it would take it below the minimum advertised price.

Definitely stupid, but it's the only way I can see of arriving at this situation.