True; but it's still not a case of the account holder's free speech rights being infringed, because the account holder doesn't have a free speech right to use FB's resources in the first place. If the police were trying to keep him from posting to his own blog on a domain that he owned himself, that would be different.
This kind of thing might be an instance of infringing Facebook's rights to manage their property how they want, if FB was being forced to give the police officer access; but that doesn't appear to be the case: FB appears to be cooperating voluntarily with law enforcement to provide this tool.
I'm not saying it should never happen, I'm saying it should be subject to due process.
I don't disagree, but the reason for requiring due process would not be to protect free speech rights for FB's users; it would be because US citizens decide, collectively, that we don't want to allow the police to have this kind of power without more oversight, even if a private company like Facebook provides the access voluntarily. I'm not sure what, if any, Constitutional provision that invokes, but I don't think it's the 1st Amendment.