IANAL, but even though this is true, Facebook could still ban accounts for complying.

They are a US company, and their TOS says they can ban an account for any reason or no reason at all. If they chose to ban anyone who shares passwords, even with the US government, even if they are Americans or not, they are within their rights as a US company to do so.

It's quite likely that any law promulgated to compel the production of passwords or any other authentication information would include language prohibiting a provider from terminating an account for complying with the law.

Then they terminate the account for no reason at all.

They probably wouldn't, as it would create a huge hassle for them when the government starts investigating.

Also, proximity in time to an event is admissible as evidence of intent.

Is it really law though, or just an option? Don't give your password and don't enter.