Apologies. I'm not a native English speaker. Still having a problem imagining in what sense an SMS service might be "publicly available", and how public availability helps in proving control of a phone number :-$
Have you visited one ? https://smsreceivefree.com/ for example. you will understand what publicly available means: they provide a phone number, you use it for whatever and check the site page where all text sent to this number are displayed.
