There are a bunch of references to "Security Credentials Management System providers" in the DOT document. So it sounds like there will be some attempt to reject self-serving incorrect data, and even a mechanism to report and exclude "misbehaving" devices. But there are lots of gray areas and value judgements in what's allowed to be sent.
The message types are interesting to read (second link below). I thought at first that the Red Light Violation Warning was a message where your own vehicle sends out "Hey, we're blowing this red light, everybody watch out!" But I think that one is intended to be sent by the traffic signal system. But still, if you aren't in control of what your vehicle sends, what's to stop it from broadcasting data you don't want it to send, like "Hey, we're exceeding the speed limit by 17 mph"? Another value judgement that seems like it would be made at some regulatory level. Even if the messages are completely anonymous as claimed, you probably (at a personal level) don't receivers to clue in traffic police to show up further along your route, or have insurance companies try to match those with private roadside license plate reader data. At a societal level I'm sure some people would favor that, and others wouldn't.
https://www.its.dot.gov/resources/scms.htm
https://www.its.dot.gov/research_areas/cybersecurity/scms/SC...