Ambiguity, or not?

Don't worry, bureaucrats bribe.

I can't help feeling that that is a little contrived.

I am not sure I am prepared to go so far as to say that bribe is a transitive verb, but if bureaucrat is to be the agent of the sentence I feel that you need to state who it is the bureaucrats are bribing. The phrase bureaucrats bribe only seems to fit naturally in a sentence such as Politicians lie, bureaucrats bribe.

If bureaucrat is to be the patient, then I have to say that I think it is pushing the English language where it is not yet ready to go, advertisements for soup notwithstanding.

Just one more comment.  There is one point not mentioned yet. I just found out about it today. I want to add the following thing:

There are certain modds existing as you all know.
Active - The man shot the soldier.
Passive - The man was shot by the soldier.

Middle ( Medio-passive ) - This book reads easily.

Coming back to the sentence: Sheila seduces easily and willingly

Another explanation of what happens when reading or hearing that sentence is that it reminds you of a middle construction. This is due to the fact that the adverb "easily" follows the verb. When "willingly" follows the verb, an interpretation that demands an agent is needed. The same applies to "Bureaucrats bribe easily".

That´s all I wanted to add.....

Maybe I wrote my last statement in a way that wasn´t that clear and free of ambiguities as well.
I just wanted to say something about the sentence the whole discussion started with. It seems to be quite clear to me, and as far as I can see to the others as well, that easily allows a different interpretation. And I still believe that in the sentence in question the middle construction ( medio passive ) is a good explanation for that ambiguity.
I believe that the sentences included in the post done by milky are agents, except the door example. Well, by the way, this depends on the situation. "Doors open willingly" reminds me of the door described in one of the "Hitchhiker´s Guide to the galaxy" books. This door opens willingly by itself.

Well, an agent is someone who does something actively. In your cases the patient submits willingly, therfore he is the one who does something. He is not the patient in this case ( patient refers here to the thematic role ) He decides to submit willingly, therefore he is an agent in this case. This applies to a certain extend to all your three cases. ( Let´s  assume that the door in this example is taken from the book already mentioned, otherwise the "Doors open willingly" -  sentence is a medio passive construction as well. At least as far as I can see.). But this one seems to be context dependent in my point of view.