Task visibility in Activity section

Hi All ,

I do have one requirement where the completed task should be visible to Opportunity owner user on the activity section but  few task we are automatically assigning it to group in which it is not showing " "Group had a task "  rather its showing like below image 

so is it because the user is not a member of that group .??

if i logging as member of thatgroup I am able to see  like "Group had a task"

Any Salesforce limitation are is it standard behaviour??Any document!?

Thanks in Advnc!