I saw the free speech angle as related to the government’s ability to go after Twitter, and this user. (But I agree with GP that the point is moot if they impersonated the FBI.)

I don't see any reference to the 1st Amendment in the parent comment.

Rather, this is a better analog to shield laws, which can protect media from divulging sources in many cases.

OP mentioned free speech and Twitter is using free speech in their legal defense.

In the argument you made, private versus public is entirely irrelevant.

There are two free speech arguments. Keep in mind that "free speech" is not relegated to the 1st Amendment and defenses of that generally lean on supplementary law.

1) The free speech of the user. Again, while it's true that it's not protected within a private entity, it's irrelevant because your protections are limited; in this case when your speech breaks another law.

2) The free speech of the platform. Being compelled to reveal this information really doesn't even touch any free speech argument except a vague interpretation of shield laws. DMCA as it exists provides legal protection against the crime, of course.