I have several pivot tables spread across several sheets that I have formatted without any border. Whenever I add or change values on the table they point to and then do a "refresh all", the pivot tables suddenly have thick borders around them. If I remove the borders and do a "refresh all" again they do not reappear unless I add or change values again.
I have the "preserve cell formatting upon update" option checked. I tried unchecking it but when I do that the pivot tables return to their default format and I lose the cell color and font formatting that I have applied to the table.
This only seems to happen to me with sheets that at one time had a pivot table on them that did have a thick border around them. Once this happens, every pivot table on that sheet exhibits this problem. I would replace the sheets with fresh versions that have never been formatted with a thick border but that would mean re-creating every table.