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I've mentioned this in a past reply thread but I later found out it's actually more straightforward than this. Someone else posted this image which shows you the status which is attached to a calendar event:
You want to make sure that you set that to Free if it's an out of office appointment you're sending to other people. Then, once you send it out, you can edit the instance for yourself only (don't send updates when you save it) to mark it as out of office. That way everyone else sees your out of office notice so they're reminded of that but it doesn't make them show up as out of office themselves.
If someone does make this mistake you can also just fix it yourself by editing your instance of it to show free.