It matters significantly.
When police are dealing with a private compny there are a couple of different ways to approach it.
Provide a order under a section of the law, and order the company to comply. In most cases, this would require a judge to hear arguments and issue an authorisation. OR
Ask the company politely to do it, in which case the company can choose whether (or not) to comply. Because it is a private portal, no right to free speech exists (facebook can censor you for whatever reason they see fit).
The second case is what appears to have occurred in this case. Facebook decided that everyone was best served by not having this played out on Facebook, so disabled the account to minimise the risk to the lady in question, her child, the police, any people that came to support her, and the public in general.. (can you imagine what could have happened if some of those people egging her on had turned up with guns of their own??)
A better example would be You and a friend are living in a house... Your friend decides to do something illegal, and the police knock on the door. You answer\, and agree to let them in, at which point they see evidence that implicates your friend. Because you voluntarily let them in, that evidence is legally obtained.