Not to belabor the point: Delete means delete (via the key which reads 'delete'). Trash or drag to trash +/- empty trash means something else (ie, what it says).
I've never considered delete and trash to be synonyms; and probably I've never thought about the issue (until now) when I've gotten rid of a file by dragging it to Trash. My bad.
As I said, your literal interpretation of the proffered advise was on the mark.
But neither trashing files nor emptying the Trash is, as a rule, necessary to reach your end in instances such as this; as a matter of fact, we generally advise users to drag files to their desktop to test whether or not they need to be trashed rather than immediately trash them.
(This is the first instance I recall running into in which a user was prevented from deleting a file without being offered the opportunity to authenticate.)
