A direct message would have been at the door and said: “Please stop throwing paper on the floor, there's a wastebasket on the other side of the room”.
(I also suspect that the reaction would have been at least somewhat more positive.)
"Please discard paper towels into wastebasket" is direct and specifies exactly what kind of behavior is desired. Your example doesn't do that. It says there is a wastebasket, but the only request is not to throw paper on the floor. It could be satisfied by leaving the wet paper towels on the sink, leaving them draped on the door handle or slapping them on the wall. (How's that for passive-aggressive!)
The original message is both shorter and clearer. It's both pro-active and respectful. Getting angry at the notice and littering to show you won't tolerate "condescension" is just being a dick.
Whichever the case, I hope you can accept that a great number of people, when in the described situation, will not think the message “pro-active and respectful”. Is their dickish response justified? No, but it is what it is.
However, the general idea of reducing the friction involved with following the rules is good. Having laws (such as those related to "piracy") that are openly ignored has a corrosive effect on a society's respect for the law in general. For the most part, I agree with Larry Lessig's comments on that matter.
What irks me is that everyone thinks they're psychologists so they throw around clinical terms like "passive aggressive" which they have right to use. No more so than a layperson trying to sound intelligent by using terms like "exponential complexity"...
In regard to the article, my take-away from it is that all the media industry needs to do to lessen piracy, is make their content easier to access legally - not make it more difficult.
1. it asserts authority ("right") rather directly addressing the underlying issue (the concerns the users of the bathroom have with hygiene and "pragmatic" efficiency)
2. it ends with the line, "Thank you for your co-operation", which is offensive and condescending because the author of the sign expects co-operation and consideration without offering any in turn because they are "right" (when clearly the target of the message doesn't care what's "right")