My assumption was that tagline meant what to said, that it didn't matter when you create or publish something, that the government was open to giving a monopoly to whomever jumps through the legal hoops first.
...which has been a major load of salt I've carried around with me.
First-to-file and first-to-invent are instead what happens if you get two different people who try to file for a patent before that point. In a first-to-invent system, there's an adjudication process that's going to look at all of the internal records to figure out who "invented" the process first (which, in the absence of evidence, is going to default to the first person to file anyways). In a first-to-file system, the first person to get their paperwork in the door is going to get the patent.
This doesn't mean that an unscrupulous person gets to look for public disclosures and rush their own patent applications to beat out the original inventor. You still need to demonstrate independent conception of the idea (although this would likely only be demonstrated in the context of an actual trial).
[1] I don't remember it's length, but I want to say it's like a year.
There are nuances however with prior-filed patent applications. While such applications are not immediately public, once they are published (typically 18 months after filing), they become prior art retroactively, as of their filing date.
Even if a person independently conceives of a patentable idea, they shouldn't be able to get a patent for it if there exists prior art (although it obviously happens sometimes because the patent examination process isn't perfect).
IPRs and PGRs can also be used for this, and are cheaper than doing it at a full-blown trial.
These rules only apply when two people with the same invention both file a patent. If you publish something on Monday and someone files a patent (really - a provisional) for it on Tuesday, you are prior art to their patent and can be used to make it "obvious."