Short answer: You need to give visibility to all items related to the activity (deal and related contact person and organization).
When you create an activity, the activity may be related to several different items. The assigned user needs visibility to all of these items.
First of all, make sure that the assigned user has visibility to the record you've assigned the activity to. If you're sure they have visibility, then make sure they have visibility to whatever else is related to the activity.
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