deleting and editing attachments

We have encountered such a problem, in which we can not see any dependence either on the side of permissions or on the sides of profiles. 
We have a problem with deleting and editing attachments in the test case tab
Some see deletion options in each line, the creator sees only the last two, even the admin profile does not see more.

 

Our administrator profile has such rights and yet in some cases, we do not know the dependencies of which, the delete icon is not available. The same is true of the creator, sometimes it can't delete its own and can easily delete someone else's.

Today we noticed a certain regularity
1. when we open the attachments tab the deletion is visible. 
 
2. Add a new attachment
 
3. We do a refresh
 
4. then it is possible to delete the old one and it is impossible to delete the new one. This changes as you refresh. 
 

This is a bit incomprehensible to us. Referring to the static answer something is deleted when adding a new one on the server?