Please check the rights from the perspective of the user:
Your user seems to have too many rights. Therefore you have to check the user.
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You probably have not only the other person’s calendar in view, but also your own.
So you will add an appointment in your calendar where you are not a participant. You are then the owner, but not a participant. So you will only see the appointment if you display the appointments you are the owner of.
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Yes, you are the owner of an (appointment) data record if you have not explicitly entered it with the appropriate rights for/at a user.
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see 1.
Please check also:
Select only a user. Nothing else.
Did you can create an appointment (in the users calendar)?
What do you want to do anyway?
Stefan