A public disclosure by a first inventor prevents a later inventor from receiving a patent on the same invention. Even if that publication happened only one day before you file your application and you had no chance to be influenced by it at all, you will not get a patent (or it will be held invalid).
Saying that first-to-file means a non-inventor can lawfully obtain a patent is also wrong. It seems to imply that a new, non-obvious invention can only be made by one person at a time. This is not true in competitive industries where many people are working to solve the same problems and will often come up with the same new solutions independently. First-to-file encourages them to apply for their patents early.
There is such a thing as "public domain" inventing, as you call it. It is simply done by (1) inventing, (2) publishing, and (3) not applying for a patent.
False. A recent U.S. decision holds that such a disclosure must be well known to practitioners of the art, not just known to a few! Publication is no longer sufficient.
You do have to lie and say you thought of it independently; something impossible to disprove. The number of people who'd lie for big money is... innumerable.
You can patent ideas thousands of years old - if they're not well known to practitioners.
You're right that any publication will not be sufficient. A publication needs to be discoverable by the practitioners of the relevant art. However, it does not need to be well-known to them, nor does it need to be actually known by any of them. It only needs to be reasonably discoverable.
Saying that first-to-file means a non-inventor can lawfully obtain a patent is also wrong. It seems to imply that a new, non-obvious invention can only be made by one person at a time. This is not true in competitive industries where many people are working to solve the same problems and will often come up with the same new solutions independently. First-to-file encourages them to apply for their patents early.
There is such a thing as "public domain" inventing, as you call it. It is simply done by (1) inventing, (2) publishing, and (3) not applying for a patent.