I'm not familiar with the specifics of the law, but my guess would be that it does not require that something be deleted upon any delete button click. I would assume it requires full deletion when requested through proper channels.

There are plenty of cases where a system would not function correctly if you are actually erasing DB entries when a user clicks the delete button. In many cases, even the users themselves might expect to be able to undo or go to a delete list and see entries that were deleted.

At my company, I heard them discussing deleting the data the user requested within 1 month.

Oh, my bad, I misunderstood your sentence.