That question has a complex answer. In short: not really.
Unfortunately, I know a little too much about phone networks to have a representative answer. I know very little about Facebook, except that its users usually attribute to it more privacy than it really offers. Trying to understand why that is is the reason for my question.
Yes. On one hand there are quite strong laws about privacy for phone companies and second I pay them. By contrast, I would not pay FB even if I had an account. Their entire business model is, that they are selling private data. ( Technically it is unfortunately neither for FB nor for telcos a problem to eavesdrop.)
There's an illusion in online communication that makes the average user think any particular message they send is like physically handing a message to another person. Using Gmail as an example, sure, your email goes to the right person, but you first send it to/through Gmail. They just happen to pass it along to the recipient.
I consider FB chats to be much less private because they actually get stored on a server somewhere by default. Also I can access them anywhere with an internet account. Neither of these things are true of SMS.
AT&T cops to saving SMS messages, not just "pen trace" (sender/recipient data), for up to 72 hours. For "delivery purposes" only. Though the release I read doesn't specify to whom.
If I log in and click the Messages button I can see all my messages. To do that they have to be on their server. There isn't an off-the-record button I missed is there?
It would be covered under the Stored Communications Act. Unfortunately reading the act it looks like it is up for debate as to whether they are breaking the law. The Stored Communications Act allows voluntary disclosure when two things are true:
1) The communications were inadvertently obtained and
2) The communication appears to pertain to commission of a crime.
I don't think you can classify this as inadvertent. So I wonder if Facebook can be sued.
There is one way to find out. Create a decoy post, hear from law enforcement, and sue Facebook.