If the string property containing a marking has kept the default Copy to Reservation setting of True, then a user who has Use Marked Objects but does not have the Add Marking permission will not be able to check out a document, even if the user has Full Control of the document itself.
This is by design, since to checkout a document creates a new Reservation document which must have the marking on it due to its property's Copy to Reservation value of True. This requires the marking to be "Added " to the new document, and since the user in this scenario does not have the Add Marking permission, the checkout will be prevented.