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.
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.
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.
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?