Who is responsible to register work estimates during the sprint?

Hi folks,
there is a question in the open assessment:
Who is responsible to register work estimates during the sprint?
Correct answer is Development Team.
Product Owner is false.
I see a contradiction here.
Yes, the Dev Team is responsible for all estimates.
BUT the question is not about giving estimates, but about registering them (writing them on the story card).
Scrum Guide:
"Product Backlog refinement is the act of adding detail, estimates(!), and order to items in the Product Backlog. This is an ongoing process in which the Product Owner and the Development Team collaborate on the details of Product Backlog items. [...] However, Product Backlog items can be updated at any time by the Product Owner or at the Product Owner’s discretion."
This means, either both answers are correct (collaborate) or Product Owner is correct (can be updated at any time means he can change the estimates at any time). As of the Scrum Guide, there is no way only Dev Team should be correct.
I suggest to change the Scrum Guide (exclude estimates from the things PO can update) and keep the question as it is.
Best, Ludwig