Influential members such as yourself and others that feel the same way can easily speak up against them and force their hand to rectify the situation..
There's not much that one can do when the manager or campaign in question either:
1) Acknowledges the problem, but effectively does nothing.
2) Completely dismissed your PM and/or ignores it.
Trusted/influential member: "Hey guy..If you don't stop the spam emanating from the campaign you manage I'm going to leave you red trust and go tell your boss to fire you.."
The question remains whether the usage of negative trust from the default trust network is appropriate for something like this this.
But if 1 person the DT list went out of their way to leave negative feedback on lets say, 100 members in active signature campaigns than this would make them be kicked out of such said campaign because 99% of them do not allow "red" members to participate. But if the "red" is not clearly justified and this is all done in one day, I think issues would arise for such DT member